The point of view of this story is that of a third person narrator. The story is not told from the point of view of Madame Loisel or anyone else who is actually involved in the story. Instead, it is just some uninvolved narrator.
The narrator is omniscient. The narrator can see what the characters are thinking, although this ability is not used much in the story. However, we are told, for example, that Madame Loisel is not happy because she thinks she has married beneath her -- that she married someone who was not high class enough for her.