The only conflicts that get resolved in the short story "The Necklace" are the external ones. The external conflicts of the story are based on the necklace itself, namely:
1. How to secure the necklace/jewelry? -- Going to Madame Forrestier to borrow one of hers.
2. How to replace the necklace once it was lost? -- Losing all of the marital money in an effort buy a replacement. Using up all of their savings, moving to a smaller apartment, keeping the secret of the lost necklace, and then paying for it for years.
Sadly, the internal conflicts of the story remain intact, which is where the tragedy of the story actually stems from. The internal conflict is that Madame Loisel is an unhappy wife who wishes to have riches and fortunes for herself. While that, in itself, is not a bad thing, her desire for bigger and better things renders her unable to see what she actually does have: a good husband, a livable home, and she even has a maid to help her around the house, which is interesting since Madame does not make a living of any kind. Therefore, her genteel poverty is at least something much better than the tragic changes that were about to go her way.
Another internal conflict is the state of the marriage. Monsieur Loisel is obviously either too blind, too obstinate, too ignorant, or too unintelligent to see what is unfolding in front of his very eyes. His wife is extremely unhappy but she is also ungrateful and obviously lacks a lot of gusto for everything. Perhaps this is one of the expected behaviors of Victorian wives. Nevertheless, he still goes along with everything his wife says and wants to a high cost to him.
The last internal conflict that goes unresolved is Madame Loisel's dissatisfaction with her life. Despite of the ball, she is an unrelentingly unhappy woman. Perhaps she finds satisfaction in misery. Regardless of what happens to her, and whatever she does, she continues to be miserable. This is an internal conflict that never gets resolved in the story, as we are only left with the information that Madame was informed by her friend, Forrestier, that the necklace that Mathilde has sacrificed so much for is nothing but a fake.