What is the most important element in the short story “The Necklace?”

It's not possible to provide a definitive answer to this question. There are many important elements to "The Necklace," which is one of the reasons why it's such an exceptional short story. However, I would like to suggest one important element is the picture the story paints of Parisian society at that particular time. We gather from the events as they unfold that society in late nineteenth century Paris was one in which status was everything. And Mathilde subscribes to this notion wholeheartedly. Despite leading a normal, lower middle-class existence, Mathilde thinks of herself as entitled to better things, believing that she has noble blood in her veins. It's essential for her to be seen as socially respectable, to partake of the finer things in life. This, she believes, is her due.
So the Education Ministry ball allows her to live out her dreams of mixing with the upper echelons of society, where she feels completely at home. But Mathilde's aspirations of social climbing are as worthless as the fake necklace she wears to the ball. Indeed, the phony necklace perfectly symbolizes the inherent worthlessness and vacuity of the desire for elevated social status and the extraordinary lengths that people will go to be accepted as part of the social elite.