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Few parts of the graduate program at UCSD spark more fear for no reason than the language exam. Mathematics seems to be one of the last of the technical fields to have held on to this relic of an academic requirement. UCSD used to require two languages, but legend has it that former head TA Cameron Parker lobbied sucessfully to change the requirement to a single language. These days few faculty care about the details of this exam, and there are no published standards.
Officially, you may take the language from any faculty member you can convince to give you an exam. You may take the exam in one of French, German, or Russian, or petition for another language if you think there is a special need (Hungarian, say). Typically this test involves being handed some text to return translated at a later date, with perhaps a spot test of your translation. Unless otherwise directed, you may use any resource not prohibited. The exam is nothing to stress over. If you know any Romance language there is no reason to hesitate getting this over with quickly; indeed there is no penalty for failure. For French language exams the Davis math department has an online mathematics dictionary. Bon chance!