In "The Necklace" by Guy de Maupassant, the narrator refers to the main character as Madame Loisel until she meets the woman who had, ten years before, lent her the necklace. After Madame Loisel and her husband have lost everything in trying to pay back what it cost to replace the necklace, life has been very hard on them. Madama Loisel is no longer young-looking and beautiful. She has a worn look about her: life has taken a great toll on her.
Madame Loisel approaches her friend, Madame Forestier, who had let her borrow the diamond necklace in the first place. Madame Loisel calls her "Jeanne," who at first does not recognize her old friend, and is surprised that she would be addressed so familiarly by a "plain good-wife" (who she believes she does not know). When Jeanne recognizes Madame Loisel, she refers to her by her first name, Mathilde.
There could be several reasons for this change. The title "Madame" may up until this point been the only part of Madame Loisel's past and former station that Mathilde has been able to hold on to.
However, Jeanne's overall reaction makes me believe that "Madame Loisel" made yet another error. Jeanne was her friend: friend enough to lend her a beautiful necklace. Jeanne still sees her as a friend by calling her Mathilde, which denotes that Jeanne accepts her for who she is, even in plain and poor clothing. With that said, the truth about the necklace—that it is a fake—shows Mathilde that she was mistaken about Jeanne. She thought Jeanne had great wealth, and she may have had some money, but the illusion of her success was generated with diamonds made of paste (or glue). This also suggests, in listening to Jeanne's impassioned words of sadness, that all of this suffering has been for nothing.
"Oh, my poor Mathilde! How you are changed!"
Madame Forestier, deeply moved, took her hands.
Had Mathilde really been able to "see" her friend, rather than to a social superior, she might have felt comfortable discussing her dilemma and might have made arrangements to replace the piece over time, had the jewelry been real. Because it was not real, Mathilde would have saved herself and her husband great hardship (and she might have learned an important lesson). However, referring to the theme of "appearance vs reality," Mathilde was no more able to spot a true friend than she had been able to spot fake diamonds—for all she saw was what she wanted to see, rather than what truly mattered: she had a loving husband, a comfortable life and a friend who probably would not have cared even a little if Mathilde did not have the money and social standing that Mathilde felt she had to have.
It should be noted that the ending of "The Necklace" shows Maupassant's mastery of the craft of storytelling. He dramatizes the revelation that the necklace was only made with imitation jewels and that Mme. Loisel has grown coarse and ugly while her friend Mme. Forestier is
...still young, still beautiful, still attractive.
Maupassant takes pains to set the scene. It is a Sunday. Mme. Loisel had gone for a walk along the Champs-Elysees. This is a place where it would seem plausible for two women of different social classes to bump into each other. Maupassant makes the scene dramatic by describing Mathilde's inner conflict. She doesn't know whether she should speak to her old friend, but she has gotten bolder with the life she has been forced to lead for the past ten years. She decides not only to speak to her but to tell her everything about the incident of the lost necklace. In this scene it is as if she relives that terrible night and the ten years of toil that ensued.
Because the final scene is composed mostly of dialogue, we can visualize this encounter. Maupassant chose the perfect way--out of many possible ways--to deliver the shocking information that the diamond necklace was a fake.
The narrator does not call her Mathilde because that would be inappropriate for an anonymous third-person author to do. Both her husband and her friend (whom she surprises by addressing her familiarly as "Jeanne") call her by her first name, however.