The character traits that describe Mathilde Loisel are in no way redeeming. From the very start of the story we realize that not even Maupassant has the intention of making a likable character out of her. With the exception of her "pretty" looks, Madame Loisel does not have too many extraordinary personal characteristics. In fact, she may actually come off as follows:
Falsely entitled- The story establishes that Mathilde was not born into a rich or powerful family. She had no dowry, so she could not "select" a rich husband to join fortunes with for the future. She, instead, is married to a clerk. As such, she is unhappy, dreams of riches and fortunes, and truly believes that she deserves better. Why would she believe something like that if she has never seen any difference. This shows you that she may have a false sense of entitlement that leads her to believe that she is better or more deserving than what she is. The problem is that we do not see any quality in Mathilde that would support such theory.
Vain- Mathilde wanted all the attention of the ball to fall on her. For this reason, when she goes to ask Madame Forrestier for a borrowed necklace, she chooses one that goes perfectly with her personality: the most flamboyant, flashy, showy...and fake-looking in her friend's collection. She picks it up because she feels that it will make her look better than the others at the ball. In reality, this was one false piece made of paste gems that she ended up paying dearly for.
Unsophisticated- Mathilde may have wanted all the riches in the planet, but she did not know much about them. She would have known that the necklace was fake, or at least she would have known how to ask the question, had she been more worldly. She would also have shown some elegance and dignity if she had confessed to her friend what happened instead of going by what her pride dictated.
Ungrateful- She was not thankful for the little that she did have. Notice that, after working to replace the necklace, she went into a worse lifestyle than she had before. Her husband had to give up whatever small inheritance he may have gotten. They had to dismiss their maid, move to an even smaller place, and she was visibly shaken as well as mentally affected. Yet, not even when things were better was Mathilde even the least thankful for anything. Not even when her husband secured the invitation to the ball.