I would say there are several themes in this little story. To name just a few, there is a theme of vanity and entitlement, a theme of materialism ending badly, and a theme of dishonesty coming at great cost.
Madame Loisel is a charming and pretty young woman. She is fully aware of this. And she believes that this entitles her to a better life than she is presently leading, more wealth, a superior social life, and even a better husband. It is this belief that causes her drain her husband's savings account, borrow a necklace, and dance the night away heedlessly, thus losing the necklace, and then lie to her friend. This sense of entitlement could be said to have been her downfall, as could her avid materialism, which has made her completely discontent with what she does have. Similarly, her dishonesty is largely founded on caring passionately about what others think of her, seeking admiration from all, even to the degree that she cannot bring herself to tell her friend that the necklace has been lost.
Madame Loisel condemns herself and Monsieur Loisel to long years of labor and poverty, all because of her vanity, sense of entitlement, materialistic values, and dishonesty. Du Maupassant's themes are a series of object lessons that transcend time and place.