The MLAC (Mouvement pour la liberté de l'avortement et de la contraception, literally "Movement for Freedom of Abortion and Contraception") did exist from 1973 to 1975. At its peak, it had more than 15,000 members.
Rosemary Standley playing Monique and who sings during Annie's abortion is actually a professional singer and guitar player. She also sings the song during the closing credits, which is the hymn of the MLF (Mouvement de libération des femmes, literally "Movement of Women's Liberation").
The town where the action occurs is not identified on purpose: it could be anywhere in France. For memo, the movie was shot in small towns in the Paris region.