Many modern American readers of both sexes may like this story because they can relate to M. and Mme. Loisel. Millions of Americans have gotten themselves in serious debt because of living beyond their means. They buy big houses with thirty- and thirty-five-year mortgages, then fill them up with furniture and appliances, and of course they have to have a couple of new cars in their double-garage. Maybe even a swimming pool, a covered patio, professional landscaping. Once they are deep in credit-card debt it is very hard to get out of it. Instead of paying the debt down, they increase it by borrowing money on one card to make a payment on another card. These debts are called "revolving balances," and the debtors begin to feel themselves revolving helplessly round and around in a whirlpool that is threatening to suck them down. They realize that it is their own vanity that has entrapped them, just as it was Mathilde Loisel's vanity that got her and her husband into such serious trouble in nineteenth-century France. For modern Americans their big homes can come to seem like prisons or forts. They hate the meaningless oil paintings they bought to mitigate the glaring whiteness of the plasterboard walls. They begin to realize that the big, gaudy furniture they bought to fill the enormous rooms is made of plywood and compacted sawdust, and it is like everybody else's furniture in the neighborhood. The Loisels were not so different from many people today.
Guy du Maupassant's "The Necklace" has been defined as one of the most "widely read and anthologized" short stories (eNotes "The Necklace" Study Guide-Introduction). Given the subjective nature of the question, numerous reasons can be given, and supported, regarding the popularity of the tale.
First, the ending of the story proves surprising to many readers. Readers, under most circumstances, like to have endings which are unexpected. Readers may become bored if they know exactly what will happen next. Second, readers may tend to have the mindset that bad things which happen to others is better than when it happens to them (a sort of "better you than me" mentality). Third, some readers like to see people punished for their misdoings. Given that Madame Loisel acted horribly toward her husband (ungrateful), some readers may feel as if the punishment was appropriate (she deserved it). Lastly, many people may like reading a text such as "The Necklace" because it emphasizes a moral lesson. Moral lessons are timeless, and the text's moral lesson makes the text timeless as well.