Qualifications
Believe it or not, what kind of degree you have or whether you have one at all isn't the key in getting a gig with the Foreign Service. There is no particular educational requirement, but there is an exam, the Foreign Service Exam. It covers a multitude of subjects such as history, geography, economics, government, English, and even popular culture. This test is your gateway to working in foreign lands. Pass it and you've got a shot. Fail it and you don't. It's pretty much that simple. And it isn't easy either; it's hundreds of questions long. According to one career diplomat, the best way to prepare for it is to simply be a well-rounded student and take classes on a plethora of subjects.
Disclaimer: While you may be able to get in without a degree, having one doesn't hurt and can certainly help.
Non-tangible qualities that may not be qualifications, per se, but probably make foreign service a lot easier are a desire to travel, a sense of adventure, willingness to be independent, willingness to try new things (including food, culture, and language), and, depending on where you're assigned, the ability to operate effectively without being able to engage in what one might call "regular hygiene."