What is the paradox in the story "The Necklace" by Guy de Maupassant?
I am asked to compare the paradox of this story to another short story, but I cannot figure out the paradox. Is it just that from the middle class she ended up in poverty?
I am afraid you seem to have confused your literary terms somewhat. A paradox is defined as a statement or a situation that seems to be a contradiction but reveals an inner truth. Consider referring to someone as a "wise fool," as Viola does to Feste in Twelfth Night. This is a statement that apparently makes no sense, yet when we think about it we can see the truth that emerges from this paradox.
What I think you are talking about is the situational irony that lies in the ending of this excellent short story. Situational irony occurs when there is a contradiction between what we expect to happen and what really takes place. We can see the massive situational irony at the end of this grimly humorous short story when we find out, after Mathilde Loisel reduces herself to an "old woman" because of the hard work she has been forced into, discovers that the necklace was only fake after all and she has suffered needlessly:
Mme. Forestier, quite overcome, clasped her by the hands. "Oh my poor Mathilde. But mine was fake. Why, at most it was worth only five hundred francs!"
This is the massive situational irony that gives the story the great impact that it has, and we are left questioning whether poor Mathilde deserved what she got for her constant daydreaming or whether she has suffered unfairly. If you are after another short story to compare this one with, "The Gift of the Magi" by O. Henry is another excellent example of situational irony.