First-Person (Peripheral Narrator)
In the classic French style, Stendhal gives us a narrator who is clearly speaking in the first-person, but also has omniscient knowledge of the characters in this book. He even inserts himself directly from time to time, saying things like,
How many times, dreaming about Parisian balls long left behind, with my chest pressed against those great blocks of stone—a lovely gray streaked with blue—has my glance plunged down into the valley through which the Doubs runs! (1.2.3)
But even thought he uses "I," he knows absolutely everything that the characters in this book think and do.
So how, you ask, can a first-person narrator claim to know everything? Well here's the weird part. Stendhal's narrator actually admits to the fact that he's a guy who's making up a story as he goes along. At one point he says,
Writing these things, I know, will still further injure this unfortunate author. Prigs and prudes will accuse me of indecency […] [Mathilde's] a completely imaginary person. (2.19.20)
So he's saying that everything in this story is make-believe. Stendhal wrote this book in the early 19th-century, long before it was cool to point out that your story was fictional. That came later with postmodernism and something called metafiction. So kudos to Stendhal for being way ahead of his time.