Supposedly First Person; Actually Third Person Omniscient
This sounds quite odd and complicated, and it kind of is. In the first chapter, we have a mysterious, nameless, faceless first person narrator (supposedly a former classmate of Charles Bovary) who recounts the first time Charles appeared in boarding school. However, this is not your average first person narrator. We don’t know anything about the guy, and he doesn’t make a single appearance in the book. Furthermore, he knows everything about Charles. This makes for a natural transition into the narrative voice of the rest of the book; from Chapter Two on out, we see things through the perspective of a third person omniscient point of view. But again, this is not simply an average outside observer…we get a deeply personal, intensely internalized view of the characters.
The point of view of Madame Bovary was pretty radical when the novel came out. Flaubert delves way down into the psychological depths of his main character, and we emerge with a portrait of Emma that is unflinching in its directness. We can look at her objectively and be like, "You brought this all upon herself," but at the same time, we feel her pain; we experience what she experiences and understand why she makes the decisions that she does. We can see why Flaubert himself famously claimed, "Madame Bovary, c’est moi" (I am Madame Bovary). By the end of the book, we readers might also say, "We are Madame Bovary."