Paris to Budapest: Ryanair or easyJet or regular carrier?
Check bahn.de for train options, but that's going to be a long and expensive journey. Train is a good option in western Europe. In former Est-block countries (except East Germany, obviously) high speed trains aren't there yet.
For planes, chose airport/time convenience depending on price (including options if needed). For a 2 hours flight, even Ryanair won't be that bad. As for IRROPS, worst case scenario, they will give you a hotel for the night, plus some compensation. Unless you are trying to catch some long Gaul flight from BUD the next morning, you won't have to buy any new tickets. Google EU261 for details on care and compensation.