I could be wrong but I believe most countries on the continent ban the use of air-rifles for hunting – even small vermin. That was certainly the case in Spain. I think that the permited power levels may also be lower.
Taking it in/out of the UK shouldn’t be a problem, there should be a guide on the airline/ferry/tunnel website and I think you probably have to declare it, but having it chrono’ed by a reputable gunsmith and having that doc/report with you should help ensure that on entry no one questions its power and asks to see your FAC for it.
Go and do a search on the airgunBBS, someone will have asked this there.
You may just wish to buy a cheap plinker in France…
edit: beaten to it 🙂