Can I put that I was in French class in my common app activities section? It gave me the option to choose a foreign language and I put work outside of school to learn it.
No. That is a class. The work you do for a class outside of school is called homework, which is an expectation of all academic classes. If there is a French Club, then you clan list that in your activities.
Generally classes would be listed under course work. I think there is an expectation that all classes require outside homework. If there was a social/club component, outside the academics, then you could listed as an activity.