Has the employer (a university) broken Polish and EU law by unilaterally changing the contract without consultation and without agreement?
Unlikely, as the contract wasn't signed by both parties. A verbal agreement is just that, and they (although acting unethically) are quite within their rights to do it. Of course, there may be something in Polish law that can make it binding, but in general, it's her fault for moving before contracts were signed. I'm surprised she uprooted without a contract signed and sealed, to be honest - I wouldn't do it!
Can you tell us if it's a public or private university? The private ones are really struggling at the minute - and it would be very odd for a public one to offer a good position to someone from outside.