Foreign area officer (FAO) is something you apply for slightly down the road in your career, whether you pick Navy or Marines. So, you would commission, learn your job (i.e. get wings, SWO pin, etc.), and then do a tour or two before applying for that track.
The only straight-out-of-USNA career I can see majoring in a foreign language being beneficial for is going USMC and trying for human intelligence (HUMINT), which is an extremely competitive MOS (think 1-2 highly sought after spots per TBS class of 300). Or you could try for a SWO-Intel slot, but those are also few and far between and I don't know how much you'd use a language there.
You can take language tests (at TBS for Marines, don't know when for Navy) to get paid extra, depending on the language and how good you are. Marines get their pay regardless of where they are and what they're doing, but supposedly according to my friends who commissioned Navy, the Navy guys only get paid if they're currently using their skills. For example, in the Marines a guy who spoke fluent Russian would get his language pay all the time, but in the Navy only if he was operating near Russia and actively using the language. Clear as mud?
Bottom line: Don't plan on tying your language major (or any major, honestly) directly to a job in the Navy or Marine Corps.
