The story's title "The Necklace," is justified, because I see the necklace as the antagonist in the story, with Madame Loisel as the protagonist. It is the necklace that creates all the conflict for her. Even though, at the heart of the story is Madame Loisel's shallow love of material possessions, it is the diamond necklace that creates the tragic circumstances that lead to Madame Loisel's life of toil and struggle.
The necklace, after it is lost, becomes the central focus of the Loisels life. They must work extra hard for ten years in order to pay off the debts they incurred to pay for a new necklace for Madame Forestier. The irony is that after so many years of hard labor and sacrifice, during which, Madame Loisel grows haggard with the physical demands of hard work, her hair grows coarse, her hand calloused and tough, her beauty traded for the money they earned to pay back their loans.
The necklace was not real, Madame Forestier's necklace was fake. The Loisels replaced a fake necklace with a real diamond necklace. Madame Forestier does not even know that the necklace she got back was real diamonds.
The necklace has fooled everyone!
For you, you need to look at the symbolism in the story. The invitation, the gown and the necklace represent the desires of those of the middle and lower classes in wanting to belong to and be accepted by the upper class. De Maupassant is making his opinions known about the problems created by classes in society. The diamond necklace represents all the difficulties in society created by classes that are, in the end, all illusions just as the value of the original necklace is misunderstood. He is asking us to think about the inaccuracies in valuing someone or ourselves based on materialism.