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.