Guy de Maupassant's "The Necklace" only has three characters and very little actual conflict. Most of the drama in the story comes from one person, Mathilde Loisel, who is discontent with her life.
This internal conflict began long before she married her husband, as she always thought what she had was not what she actually deserved.
She suffered intensely, feeling herself born for every delicacy and every luxury. She suffered from the poverty of her dwelling, from the worn walls, the abraded chairs, the ugliness of the stuffs. All these things, which another woman of her caste would not even have noticed, tortured her and made her indignant.
This internal conflict continues throughout the story and shows itself in the form of pridefulness. Because she thinks so highly of herself, she is not content with anything her husband provides. This sets up an external conflict between the couple. He brings her a sought-after invitation to a ball and she refuses to go because she has nothing to wear. He gives up the money he has been saving for something he wanted to buy her a dress, but she still refuses to go because she does not have fine jewelry with which to adorn herself.
Mathilde borrows a necklace and loses it, causing a short-lived conflict between the Loisels and Madame Forestier, the woman who owned the necklace. Once they have replaced the necklace (of course they replace a fake diamond necklace with a real one), that conflict is over; however, the ten-year conflict between the Loisels and their creditors is just beginning.
He gave promissory notes, made ruinous agreements, dealt with usurers, with all kinds of lenders. He compromised the end of his life, risked his signature without even knowing whether it could be honored; and, frightened by all the anguish of the future, by the black misery which was about to settle down on him, by the perspective of all sorts of physical deprivations and of all sorts of moral tortures, he went to buy the new diamond necklace, laying down on the jeweler's counter thirty-six thousand francs.
Because they had to get the money so quickly, they had to pay exorbitant fees. They scrimp and save and work very, very hard to pay back the money—and none of it would have been necessary if Mathilde had not been so prideful.
In short, the primary conflict is Mathilde’s internal conflict which is based on her discontent and belief that she deserves more than she has. The few external conflicts are minimal compared to that.