If memory serves, the answer depends on your major and the amount of open courses you have. USNA is not like a normal college in terms of course load. Plebe year is obviously set in terms of courses for 95% of plebes. To be clear, the math course you take may vary but almost every plebe is taking some sort of 4-hour math course, chem, cyber, English, history, leadership and/or nav during the first year. Even if you validated a bunch of stuff, you are probably still locked into that general course load, though a heavy validator might free up some space in his/her second semester.
Then you need to sort out the requirements for your major. Group 3 ("humanities") majors used to have to take -- or validate out of -- 4 semesters of language. So, if you're a Group 3 major, a language, even a new one, would fit into your schedule provided you plan to take it for two full years (or you validated out of another language, thereby fulfilling your language requirement). I don't know if that requirement still exists -- sure a current or recent mid will chime in.
If you're a Group 1/2 major, you have distribution requirements in the humanities. Those can (or at least could) be filled with a language course but, in my day at least, that language had to be at the 300/400 level -- IOW, not a 101 class.
If you are Group 1/2 AND have validated a bunch of stuff so that you have extra time in your schedule AND don't want to use that time for other things such as graduate education, Trident Scholar, etc., then you probably could take the random language class here or there.
The fact is that USNA is a difficult place to learn a new language unless you're a Chinese or Arabic major, are a Group 3 major or have a lot of free time in your schedule. That is . . . [BIG CAVEAT] unless things have change a lot, which they may well have.