As an Anthropologist/Archaeologist, what foreign language should I learn in college?
You should learn a language of scholarship and/or a language relevant to a country or region that interests you.
For example, if you are interested in Africa, there would be a substantial anthropological literature about Africa written in French. In addition, French is spoken in several former French colonies in Africa. If you want to do fieldwork in an African country, however, an African language also could be useful. As another example, If you are interested in Andean archaeology, Spanish would be useful, but so would Quechua. You also might consider a language that would serve as a “gateway” to learning other related languages in a language family. For example, if are are interested in certain areas of Central Asia, learning Turkish might make it easier to learn other Turkic languages.
Another consideration would be what level of proficiency you need and whether you can put in the necessary time/effort to achieve that proficiency. For example, do you want to just acquire a reading knowledge of a language in order to read the anthropological literature in that language, or do you also need speaking proficiency in that language in order to do fieldwork. If you want to learn a non-Western language, e.g., Arabic or Chinese, are you willing to devote the extra time and effort to achieve an acceptable level of proficiency. Studying one of those languages for a couple of years probably won’t do it, and you better plan on at least three or more years, as well as studying abroad in a country where the language is spoken.
Still another consideration would be whether your future studies and career might require the ability to read a classical or ancient language as part of archaeological work. For example, if you are interested in Chinese archaeology, you would need skills in classical Chinese. If you were interested in Near Eastern archaeology, you might need skills in relevant ancient Near Eastern languages.
Since you referred to “anthropologist/Archaeologist,” I’m assuming you intend to pursue graduate studies leading to a professional career in these fields. Since academic positions are limited and very competitive, however, I still would recommend that you focus on the more widely used and practical languages (e.g., French, Portuguese, Spanish, etc.) at the undergrad level and save the more esoteric or specialized languages for grad school.