Foreign language was a mandatory class in all Soviet schools. Vast majority of schools taught English, few schools had German and even smaller fraction had French.
The allusions to French influence are everywhere in "Fathers and Sons". The novel itself is a meditation on Russian society at the time, specially the two leading intellectual camps, the established landed gentry and the young nihilists who rejected the status quo. Turgenev subtly highlights their shared francophile elements, both types usually educated in France or French schools, or taught themselves French to absorb Western culture for subversive reasons.
You can see this in the film Burnt by the Sun, which is fictional, but perhaps historically accurate in this respect. It's set in 1930's Russia. A respected Soviet military officer is eating by himself while his wife's upper-class family converses in the other room. The maid asks why, and he responds, "I can't speak French." The purpose of this scene is clear: the inability of high-status Russians to speak French is a sign of broader social change.