The exposition is mainly made up of Madame Loisel's thoughts about how she could have a better life of wealth. She laments about how she has no dresses and jewels and is left with the simple things.
The inciting action is when Madame Loisel's husband tells her he got an invitation from the Minister to his palace. Madame Loisel freaks out at her husband that she doesn't have a dress to wear. He offers to give her money to buy one.
10 years of debt...
The rising action is the events in which Madame Loisel complains about not having any jewels to go with her dress. Her husband suggests borrowing some from her friend Madame Forestier. She chooses one necklace and they attend the ball.
My necklace was only a paste!
I've spent 10 years in debt.
The climax occurs when Madame Loisel notices the necklace she borrowed from Madame Forestier is missing from around her neck.
The necklace is gone!
The falling action is when the Loisel's can't find the necklace and have to buy a replacement that cost 36,000 francs. They have to borrow money and live 10 years in debt.
The resolution occurs when Madame Loisel sees Madame Forestier after the ten years and tells her how she lost the necklace and returned her one that she bought for 36,000 francs. It is then revealed that Madame Forestier's necklace was a paste.