I found a cheap flight to Gdansk. It has a stop over in Frankfurt International Airport for about 50 minutes, where I will have to switch flights. I don't know what the gate numbers are, but is 50 minutes enough time for me to get off the airplane and go to the next gate to catch a flight in Frankfurt Airport?
You should be good. I usually fly to Gdansk through Frankfurt. The International Airport in Frankfurt is very manageable. 50 minutes should be enough if your plane lands on time.
Remember also that you won't have to pick up your luggage in Frankfurt so it will save you some time. When there is a connecting flight you have to catch, stewardess will usually announce the gates to those flights before your plane lands. ( If they don't, you can always ask them. They usually get a print out from the airport)
If your plane is delayed and/or arrives later than scheduled and you miss your flight, it is not your fault and the airport should put you on the next available flight.