There is a train from Dresden to Wrocław, the connection had been cancelled for some time but it was restored in December.
The best is to look for German tickets to Görlitz (the last station before the border) and a Polish ticket from Zgorzelec (the first station after the border). Görlitz and Zgorzelec is in fact a single town located on both sides of the border, crossing the border on this route is free of charge.
Then you will most probably need two separate tickets from Zgorzelec to Wrocław and from Wrocław to Katowice, because these connection are operated by different companies (Zgorzelec-Wrocław - Koleje Dolnośląskie, Wrocław-Katowice - PKP Intercity), and in Poland it's not like in Germany, where you can buy a single railway ticket for the whole route, in the DB tarif (or in the tarif of a given Verkehrsverbund), independent of the companies that operate the trains. If you are lucky, and buy a ticket a lot in advance, you may be able to catch one for 19 euro for the whole German section.
There is also a special offer for that train, with which for 33 euro you buy a ticket from Dresden to Wrocław valid for 14 days (trilex.de/de/dresden-wroclaw-spezial/). It may be a good option if you plan to return within these 14 days, and if you manage to buy a ticket from Frankfurt to Dresden for much a lower price than from Frankfurt to Görlitz. You must just use the search engine of the Deutsche Bahn (use the "Sparpreis-Finder" feature) and check the days you are interested in. If you depart from Poland to Germany, the ticket offer is much better, but unfortunately it's not valid when you start in Germany.
There are also connections through Görlitz/Zgorzelec where you have to change trains two or three times between Wrocław and Dresden (once in Görlitz, once in Poland, and sometimes once somewhere else in Germany). For them this offer for 33 euro is also valid.
You can also check the connections through Berlin, it's a longer way, but they might be cheaper. There is no direct train from Berlin to Katowice, and neither to Wrocław (there is a bus operated by the German railway though), but I believe that you can easily change trains in Poznań, Kutno or Warsaw.
You can also check the bus connection. They are likely to be cheaper than by train, although probably less comfortable. There is a bus of the PolskiBus company from Berlin to Katowice, and you can for sure get to Berlin from Frankfurt cheaply using one of the German bus companies (like Flixbus, Postbus, BerlinLinenBus etc.). A few days ago I made a journey from Karlsruhe to £ódź by the BerlinLinienBus and PolskiBus buses with a change in Berlin and it was really comfortable, although I was lucky that I had double seats in both buses. I know, however, that there is no cheap buses through the southern section of the Polish-German border, the only option is through Berlin, unless you combine a bus and a train connection (like a bus to Dresden, and then a train to Poland).
Websites... (in English versions)
- the German railway (Deutsche Bahn): bahn.de/p_en/view/index.shtml (use the "Saver fare finder" to find cheap tickets from Frankfurt to Dresden or Görlitz)
- the special offer for the train connection Dresden-Wrocław, unfortunately only in German (or in Czech): trilex.de/de/dresden-wroclaw-spezial/ (a ticket valid for 14 days allowing any number of journeys costs 33 euro, according to what they write there, it can be bought from the train staff)
- the Polish railway (PKP Intercity): intercity.pl/en/ (for the train connection from Wrocław to Katowice)
- the Polish local railway from the area of Wrocław (Koleje Dolnośląskie): kolejedolnoslaskie.eu/en (for the train connection from Zgorzelec to Wrocław)
Generally to find the train connection (but not the ticket prices, for that you need the links above), you can use either the search engine of the Deutsche Bahn (so the German one), or one of these Polish ones:
All three of them are able to find the trains in both Poland in Germany.
For the trains from Frankfurt to Dresden or Görlitz and from Wrocław to Katowice you should buy the tickets possibly early (they get more expensive with time), while for the train from Dresden or Zgorzelec to Wrocław it doesn't matter, the price is constant.
If you have to buy tickets for a domestic connection, by long distance trains (of Deutsche Bahn or PKP Intercity), which involves train changing:
- in Deutsche Bahn (in Germany) it's not a problem to buy them online
- in PKP Intercity (in Poland) you have to either buy online separate tickets for each train, which is normally more expensive than a single ticket for the whole journey, or buy a single ticket for the whole journey at the counter in Poland; but since you are not in Poland now, you will be able to do the second one only on the day of the journey, and buying the ticket for a long-distance train in advance makes it cheaper, so for you the better option is probably to buy two separate tickets
From the German railway, you can also buy a single ticket for the whole journey from Frankfurt to Katowice, but it will be most probably much more expensive.
For bus connections, the websites that you should check are:
- long-distance buses in Germany: busradar.com/
- PolskiBus company for cheap bus connections from Germany to Poland: polskibus.com/en/index.htm
The WizzAir company has also cheap plane connections from Frankfurt to Katowice, you should check them too. But remember that they are from another airport in Frankfurt, not from the main one, but from the Frankfurt-Hahn. For February it finds a connection for 15 euro, so it's really good option (even though you have to pay something extra for the registered luggage).
Another needed website, if you need to travel between airports or between the airport and the train station in Frankfurt, is:
rmv.de/en/ - the Verkehrsverbund (public transport union) for Frankfurt, you will find there all the local public transport connections.
An example for looking for a train connection:
You enter for example the Deutsche Bahn website: bahn.de/p_en/view/index.shtml - you enter the day for which you need the connection and the relation (Frankfurt-Katowice, just to look for the possible connection to look for cheap tickets). I understand that you mean, all the time, the Frankfurt am Main, which is a big city with a huge international airport, not Frankfurt an der Oder at the German-Polish border, from the second Frankfurt it would be much easier. So you select Frankfurt(Main), not Frankfurt(Oder). Let it be for 18th January, after 12:00:
It finds a few connections, for some of which it cannot sell tickets at all (as a whole connection) - through Berlin, through Dresden and using a direct train from... Vienna (Wien):
The connection through Vienna will be definitely expensive and complicated if you want to save money, because it's an international one through... 4 countries (you would have to go through Germany, Austria, Czech Republic and Poland), I think it's not a good idea to take it into account (although it seems to be equally fast).
What is more, it seems that the connection through Berlin might be faster than the one through Dresden (although it's the longer way)!
With the connection through Berlin it is so, that you can buy a single ticket for the whole connection in this case (for this day and this time) for 93,50 euro, but that's expensive and it's possible to save money really easily. The first option is to buy separate tickets from Frankfurt to Berlin, from Berlin to Poznań, and a ticket from Poznań to Katowice.
Let's check. We open the Deutsche Bahn website again, but now we select the "Saver fare finder". We choose the same day, and a train relation from Frankfurt to Berlin. You can also select Frankfurt(M)Flughafen, which is the station at the airport, but you should check if the ticket from the main station in Frankfurt isn't accidentally much cheaper than one from the airport - the local public transport connection from the airport to the main train station is probably quite cheap. First let's check from the main station (Hbf, it states for Hauptbahnhof, which means main train station):
You can see that dependent on the time, the prices are different (and begin from 29 euro). You need a connection which fits to the arrival of your plane and allows to travel further to Poland without excessive waiting for a train change at the station in Berlin or in Poznań. It might be so that you need to choose a train which costs 43 euro, or even 95 euro, but then (dependent on the price that is available for a train that fits you) it might become a good idea to buy a single ticket for the whole journey (the one for 93,50 euro), or to choose a bus connection. If you haven't bought a plane ticket from India yet, you can also check other days (it's usually cheaper in the middle of a week). Of course, if your plane from India doesn't get much more expensive then.
Let's check connections from the Frankfurt-Flughafen (Frankfurt-Airport) station. For me, for the same day, it finds connections, which are mostly for the same prices, but they include a train from the airport to the main station in Frankfurt (and then a change to the train to Berlin). If it's the case, it's worth to do it in such a way. If the ticket with a connection from the airport is, say, 10 euro more expensive, then... Let's check the connections from the airport to the main station in Frankfurt :-)
We enter the webpage: rmv.de/en/ and put the connection from Frankfurt Flughafen to Frankfurt Hauptbahnof (the search engines usually work so that it's necessary to put the station name in the language of the country the station is located in):
It seems that it takes about 20 minutes by an S-Bahn train and it costs 4,55 euro.
Ok, let's check the trains from Berlin to Poznań. In the same way as before from Frankfurt to Berlin, the difference is that it's necessary to select a special option for international trains. And it seems that the ticket costs 19 or 29 euro. It's possible also to check a ticket price from Berlin to Katowice, bought from the German railway. Than it is 43,50 or 53,50 euro.
So, if you are lucky, you will get a ticket from Frankfurt airport to Poznań for that day for 48 euro. Now let's check the tickets from Poznań to Katowice. Also 18th January. The webpage: intercity.pl/en/ - connection from Poznań Główny (Główny means in Polish "main", for the main station) to Katowice:
It doesn't show the prices, because when I am writing this post, they have a pause for maintenance, like every day in the night hours :-) Notmally it would show the price at all the direct trains (so not at the third one). To go it around, we can check at the rozklad.sitkol.pl page, that the distance for this connection is 343 km, and from a price list at the company webpage, we can read, that with the lowest possible discount for an early purchase of a ticket the price for a distance between 341 and 360 km is 44,80 zł. And this price would most probably show up in the search engine. 44,80 zł is something slightly above 10 euro (1 euro for the recent exchange rates is something like 4,30 zł, unless it fell and it is about 4,20 zł now).
Together it would be something around 60 euro, which is still much less than 90 euro.
There is also another, more "sneaky" way. To buy a German ticket to the last station before the border, which is, in this case, Frankfurt an der Oder (so you would need, basically, a ticket from Frankfurt to Frankfurt - I mean, to the other Frankfurt), and a second one from Zebrzydowice (the first station after the border) to Poznań - a Polish one. It's not really legal, you should have a ticket for the section between Frankfurt(Oder) and Zebrzydowice too, but as far as I know, the tickets are almost never checked on this section, since the train staff gets changed in Frankfurt(Oder), and the Polish train staff is not allowed to check tickets in Germany. They can do it after crossing the border, but then you should go to them and say that you want to extend your ticket from Zebrzydowice so that it's valid from the border (the virtual "station" Zebrzydowice(Gr), which doesn't exist in the reality, but it's possible to sell a ticket from the country border - it's not possible to do buy it online though). You can do it for free since it's within the same price list kilometer range. If you want to be perfectly legal, you can also buy at any train station ticket counter in Germany a ticket from Frankfurt(Oder) to Frankfurt(Oder)(Gr) (the German side of the border, also a "virtual" station), which costs something like 5 euro. If you like adrenaline and you are not afraid of a need for speaking foreign languages that you don't know, you can try this option out, unless it is more expensive than the previous one (it may happen so) :-)
The other option is the connection through Dresden. Which can be checked in the same way as above. But check the prices from Frankfurt to both Dresden and Görlitz. In this case it's perfectly legal to cross the border (travel on the section from Görlitz to Zgorzelec) for free, it's agreed by the railway managements of both countries that it's free at this border point. You will not find the train from Zgorzelec to Wrocław at the PKP Intercity webpage since it's a different company.
If you have some questions, ask. Sorry that I flooded you with information, but I couldn't stop myself from that, I also like railway :-) I wish you good travel.