Third Person (Limited Omniscient)
Classic Realist, and classic Flaubert. The omniscient, uninvolved third-person narrator lets the Realist author trick the reader into believing they are giving us a totally impartial, unbiased vision of the way things really are.
Here, though, things focalize totally on Félicité. She's the only one whose inner life we really get a peek at. For example, when Madame Aubain ignores her distress over not hearing from her nephew, we find out what Félicité feels on the inside:
Although used to being treated harshly, Félicité was indignant at Madame, then forgot about it. (3.39)
Madame Aubain probably doesn't know (or care) that Félicité was upset, but the narrator does and, therefore, so do we.
It's an interesting choice, because as the uneducated, kind of weird, bird-worshipping maid, most people never give her a second glance. But she's the one who outlives everyone else and has a real view of the way things are. We're glad the narrator chose her.