Does it make sense to learn any other language except English, being a mathematician? Would it be an advantage for a committed modern day research mathematicians to learn any foreign language? Are there works in Russian, French, or any other foreign language being produced or that have not been translated?
 A: Yes, there are many such works. These days, less French than Russian, but still a decent chunk of both.
A: For a lot of algebraic stuff you'll need at least a little French. Note that being good enough at a language to read a math paper with the aid of a dictionary is wildly less than the amount you need to have a conversation, so it's not asking too much for someone to pick up this ability in a few languages. Just sit down and practice through some papers where you're already comfortable with the math (say, a textbook in a subject you know very well) and you will be fine, although it will take some patience and hopefully a friend who speaks the language well.
A: 
Would it be an advantage for a committed modern day research
  mathematicians to learn any foreign language?

Knowing other languages and cultures (other than your native one) can make one a more interesting person which will certainly help during the job search phase and in general academic life.
A: From what I understand, a ton of Alexander Grothendieck's work in algebraic geometry has not been translated from its original French.  See, for example, Éléments de Géométrie Algébrique and Fondements de la Géometrie Algébrique.  
