If you need to fly as part of your European trip to cover a large distance quickly then you might want to try the following airlines in Europe, they offer cheap flights and deals which can be comparable to the cost of a train fare, just make sure you factor in all of the costs.
European Budget Airlines:
Air Berlin (German)
Blue Air (Romanian)
Fly Niki (German)
Norwegian Air Shuttle (Norwegian!)
Smart Wings (Czech)
Wizz Air (Hungarian)
We'd also recommend searching on SkyScanner to make sure you're getting the cheapest available deals.