Maupassant, the author of "The Necklace," is considered a naturalist, which is a kicked up version of realism. As such, he attempts to depict reality or actuality, with an eye on his character's plight, particularly as he/she contends with forces beyond control. As such, "The Necklace" is certainly intended to be realistic.
To examine it to answer your question, one could look at what might possibly be seen and labeled a coincidence (which doesn't work well in traditional fiction): the loss of the necklace. There probably isn't any good reason for doubting the veracity of a woman becoming so involved in her situation and surroundings that she loses her necklace and isn't aware of it. That's plausible, and plausibility is the usual test for coincidence. If something is plausible, it's not a coincidence.
I recently started my car, moved it into my driveway, shut it off and then cleaned the snow off of it. A few minutes later the car key was not in my pocket. I looked for it and never found it. I didn't at first realize it was lost and couldn't find it once I did. Mathilde's loss of the necklace is plausible.
My anecdote also leads us to a second point: not only is the loss of the necklace plausible, but not being able to find it is also realistic.
Just to throw in a third point in case you need it, Mathilde's not even thinking of the possibility that the necklace is fake is also plausible--maybe not for a wealthy woman who knows jewelry well and owns plenty of it, but for a woman of Mathilde's economic class it is. The thought never crosses her mind. She is inexperienced in the ways of the wealthy.
That final point, by the way, plays to the naturalistic aspect of the story. Mathilde is "out of her league," as they say. She is trapped by a situation that is out of her control.
I think the fact that there have been 353 questions posted in e-Notes regarding this one short story shows that many people, like myself, have been genuinely convinced that the incident described in "The Necklace" really happened long ago. Many readers, like myself, have felt deep pity for Mathilde Loisel and have spent some of our time wondering what we might have done in the same situation and perhaps even wishing we could find that fatal necklace and return it to her. It is one of the few short stories that lingers in many readers' minds. We wonder if it wouldn't have been better for M. Loisel to tell his wife that she must go to Mme. Forestier and admit the truth.
A number of correspondents have asked questions such as "What is the moral of 'The Necklace'?" and "What is the meaning of 'The Necklace'?" Perhaps the moral and the meaning and the theme and the thesis are just that it is best to tell the truth. Honesty is the best policy. As Mark Twain once said, "When in doubt, tell the truth." It was a mistake for Mathilde to try to be a Cinderella at the ball, wearing a borrowed necklace to create the false impression that she belonged to a higher social class; and it was a mistake for her to avoid confessing the truth to Mme. Forestier, that she had lost her necklace. But most of us have been guilty of similar faults. We all want to be admired for something. Below are a few pertinent quotes.
I now perceive an immense omission in my psychology: the deepest principle of human nature is the craving to be appreciated.
To be a human being means to possess a feeling of inferiority, which constantly presses towards its own conquest....The greater the feeling of inferiority that has been experienced, the more powerful is the urge for conquest and the more violent the emotional agitation.
Erant quibus appententior famae videretur, quando etiam sapientibus cupido gloriae novissima exuitur (Some might consider him as too fond of fame, for the desire of glory clings even to the best of men longer than any other passion) [said of Helvidius Priscus].
Tacitus, Historia, IV, 6.