Yes, American MDs are recognized in EU (European Union). Getting EU citizenship (you get it directly if you get a citizenship of any member state - marriage) would definitely help you, with it you are allowed to work in any EU member state. Regarding D.O. do not know, I heard there is a D.O. school near Lisbon, so I guess might be possible. However, you would have to contact every member state's medical board and inquire, since you might be required to do an internship, take some extra exams,... (even if you are an MD). If you are DO, the medical board would probably review your academic transcript to determine if you are eligible to be recognized as a Doctor of Medicine in EU. Since (from what I've heard) DO programs teach you almost the same as MD programs, you probably would.
Also, every member state has it's own matching process, e.g. in Germany there is no national match, you get an offer from a hospital for a spot and start working right away, different from US, so you would have to inquire for a job yourself.
Of course, there is always the language barrier (unless you wanna practice in UK, Ireland). In probably all member states, if you don't have EU citizenship, you are almost always required to show language proficiency. On the other hand, with EU citizenship, in many states you are not required to do it. However, in reality, if you cannot speak the language of your patients, you are not very likely to get hired.