"A Simple Heart", like most of Flaubert's work, is slam-dunk Realism, part of a whole literary movement that was happening in the nineteenth century. Its epicenter? France. Flaubert was at ground zero for Realism and we get the pleasure of seeing it here.
The idea is that the author should try to portray real, everyday life, not the sort of overemotional stuff you get in Romanticism. They would try to write down the way 'real' people talked, and they thought it was really 'real' to portray the middle and lower classes rather than nobility. So Madame Aubain and Félicité are perfect for the Realist story.