You're going to find that just about all the European airlines require you to be an EU national legally able to work in the EU. The EU countries aren't taking many immigrants, legally anyway. It isn't much different for non-US pilots to come here. Some nations are taking pilots ( ME3, China, Vietnam, Africa) but you have to have heavy jet time and an ATP with airline experience.

Check out PPRUNE for discussions with EU pilots--very competitive with far too many pilots for too few jobs. I know an Air France pilot, ex-FAF, very discouraged with the future there.

GF