This thread will give you information about converting an FAA license toa JAA licence. It is expensive and involves a good deal of hard work, but it's achievable. You may have residency and working rights in UK (and thus the EU), but you must contact the British Embassy in DC to get comprehensive and accurate information about this. Their website may have some of that information available.
The airline recruiting market in mainland Europe is not particularly healthy. Deregulation has been far slower in this area than it has in UK, and that is reflected in lack of airline startups and profits. The newly-integrated Eastern European countries have fairly active airline industries, but pay and conditions are, as yet, way behind the rest of Europe.
Look and compare very carefully the airline industry in the USA and the EU. I think you'll find there are few advantages to moving over here, unless there are family or other non-aviation-related reasons for doing so.
Scroggs