The European system is very different from the American system. General university entrance exams are required, and in some countries an additional law exam may be required, especially if it's an impacted major. Law degrees in some European countries (U.K., Ireland) are undergraduate degrees (LL.B), and require about four years of university study, a series of state exams and some monitored/mandatory internships (they don't use the word "internship", but I can't remember what it's called). In some continental civil systems, like Germany and the Netherlands, I believe it takes about six years altogether and law students will often pick a track while still in school: civil, criminal, judicial, administrative attorney, etc. Civil law degrees are essentially professional doctorates, much like the J.D. Unlike the U.S., there is little or no crossover between fields. In other words, if you become a prosecutor you will likely remain a prosecutor for the rest of your career.
The U.K. has a distinction between solicitors and barristers, although it's been substantially reduced over the last few decades. Graduates from common law countries (U.K. for example) can take the California bar without an LL.M, but I think that most civil law graduates would be required to at least obtain a U.S. LL.M first. Admissions to European law schools can be very competitive depending on the school, just like the U.S. My guess (and I could be completely wrong) is that it would be pretty difficult to get accepted to most European law faculties as a U.S. student.
Europen universities (especially on the continent) tend to be far more traditional than American schools. Since you already have a B.A., you'd be applying for something like a second, unrelated B.A. which really can't be used in the U.S. (and unless you have joint EU/US citizenship, you will almost certainly have to return after graduation.) You'd probably have a much better chance with U.K./Irish schools than with civil system schools.
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