Well depends on the flight you have booked.If you have booked any of the low cost airlines like easyjet,ryanair etc then yes they have limitations on baggage.They dont allow the 1*30kg or 1*23 kg check in baggage like regular airlines.
However if you book through regular airlines like KLM,Lufthansa,Czech Air,AlItalia,Air France then they should allow the regular flight baggage.Please check the baggage details before booking.
I travelled from Venice to Prague via Czech Air and it has 23kg check in baggage restriction per person.
Yes most of the low cost airlines in Europe ( eg EasyJet which I use very frequently) charge extra for checked in luggage . But you need to pay the same when you are booking the tickets . In case you haven't paid while you booked , then you will probably be asked to pay extra at airport . Also all these airlines are very particular about luggage size . each airlines have different dimension . Pls check that also before you travel