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You may want to check this link out: search on Facebook for Careers in Foreign Affairs. Here's the link: https://www.facebook.com/groups/careersinforeignaffairs/?fref=nf
These job descriptions should give you a sense of what degrees you need in order to be able to be competitive in that field.
Getting employment in the UN is very competitive, but not impossible. Consider working towards a degree in International Relations and continuing towards a Masters degree or law school.
The Foreign Service sounds just like what you would like. I would add considering military service after receiving your Master's / law degree as a Public Affairs officer in either the Air-Force or the Navy. You'll be able to travel the world and deal with various foreign counterparts along receiving the security clearance required to work for the State Department 's Embassies.
Proficiency in French is also required working with the UN, so consider minoring French and studying abroad if this is what you really want.