The narrator opens the story with a long look into Mathilde's lively dream world. We see all of the fancy things she desires: the Oriental tapestries, the footmen, the good food, the fancy parties. The narrator also repeatedly tells us that Mathilde thinks she was meant for a different kind of life: the lush life of high society. The opening trip into Mathilde's head gives us enough insight to form an opinion of her. And by bringing us right away into the world of her thoughts and dreams, Maupassant makes us feel as if we understand her immediately.
M. Loisel is the kind of guy who'll work long and hard to get his wife the invitation to a fancy party she's always wanted, even though he could care less about it. He's also the kind of guy who then gives up the gun he's been saving for months just to buy her a dress. Mathilde is the kind of girl who bursts into tears after getting the invitation her husband worked so hard for because she doesn't have a fancy enough dress to go in. That kind of says it all, doesn't it?
Mathilde is the classic "middle-class" woman who's bored with her average middle-class life and wants to live a rich and fabulous life. Her life is caught up in fantasies about class. Her middle-class husband, on the other hand, is a classic "little clerk" (1): hard-working, responsible, and happy with his lot. Also somewhat cowed by his wife. Mme. Forestier is the rich woman whose money enables her to casually lend expensive (or fake) jewels to friends, and to stay away from work so she can keep herself young and pretty. By the same token, Mathilde's fall into poverty seems to transform her character by forcing her to work and become less caught up in her dream world.
Loisel is related to l'oiseau, the French word for "bird." This seems a fitting last name for "flighty" Mathilde, who at the start of the story spends her days in dreamland. She wants to "fly away" from her own world and into a higher one.