How does Guy de Maupassant show sympathy for Madame Loisel in the short story "The Necklace"?
I think that he tries hard to show sympathy for her in the middle of the story, where she lives with her poverty for 10 years by saying she loses her looks (Which was pretty much everything to her) and now looks a lot older and less beautiful.
Your argument is valid, but can still be discussed from a different point of view.
If we were to agree with your statement, then the mention of the loss of the looks of Mdme. Loisel in the story "The Necklace" could certainly be seen as a detail used by the author to make his audience realize that, despite of all her flaws, Mdme. Loisel is still a typical, limited, and imperfect human being- like the rest of us are; she dreams and fails, she wants and loses, she dresses up and then loses her looks, and she can make really silly, blind mistakes as badly as any of us can.
However, the previous statement can be counter-argued by pointing out that Maupassant's use of realism is not aimed at causing in the reader any specific sentiment toward the main character. Maupassant's "The Necklace", much like his mentor Gustave Flaubert's Madame Bovary, simply tells the story of a woman who dreams above her means, that acts upon her whims, and that pays dearly for her behavior in the end. That is the basic premise of the story, and it is not told with sentiment nor decorative language; this is what makes it a true representative of the genre of French Realism.
Does this mean that Maupassant has absolutely no sympathy for Mdme. Loisel? No. Although he does not openly express sympathy, he does offer certain facts about the life of Mdme. Loisel which may inspire the audience to connect with her situation.
In the second paragraph of the story, Maupassant shows how Mdme. Loisel's problem is not simply that she was born in a poor family, or that she could not compete to make a financially-sound marriage: her problem is that she was born to feel as if she belongs somewhere else somewhere bigger and better than her current situation. That is actually what constitutes her tragic flaw.
she was unhappy as if she had really fallen from a higher station...Natural ingenuity, instinct for what is elegant, a supple mind are their sole hierarchy, and often make of women of the people the equals of the very greatest ladies
Therefore, here we have the real causative problem: poor Mdme. Loisel was born, like they say in colloquial terms, "with champagne dreams on a soft-drink budget". Had she not been born this way, she would have been satisfied with just having a home, and a good husband. Maupassant does not only use this as justification, but perhaps even as a way to tell the audience that her behavior is not motivated by avarice, but by that "instinct" that drives her actions. Maybe that could even cause some sympathy for her, after all.