What college degrees would help me move over to Europe (hate the US!)?

You need to acquire skills in a field that would get you a job overseas, and that won't be easy, because most European countries have plenty of people who can do anything Americans can do.  Your best bet would be to get a job with a multinational company that has offices all over the world.  You'd start in  the US and get transferred. Engineering, science, and technology fields would be the best choices for degrees.

I know some American scholars who teach at foreign universities in specialized humanities fields, but earning a PhD takes a long time, and there is no guarantee of a foreign appointment.

Medicine, Engineering, but you will need a job offer and sponsorship from an EU  employer. Days are gone when you can move to the EU and get a job.

maybe you can join the peace corps

Skip college for now, and go to France on a tourist visa.  Enlist in the Foreign Legion.  If you make it through recruit training (I believe about 1 in 6 do) you will be able to stay overseas.  Most likely you will be stationed in Africa, but you would reach your goal of getting away from the US.  If you stay in  the legion for a certain number of years, you can become eligible for French citizenship.