What could an American do with a bachelors in international relations with a concentration in European Studies?

You could try to get a job at the UN. International Relations is mostly for pursuing something along the foreign service lines. Working for an embassy, a consulate, department of state. You could also use it to work for a government agency.

Have you talked to your lecturers/tutors about this yet? If you did, what did they say? This may not mean much to this specific question but if you also are bilingual or have a very good command of other languages they could use you as an interpreter.....