When we talk about the "tone" of a story, we are discussing the attitude taken by the narrator towards the subject, themes, and characters. It's the impression we get about the characters based upon the narrator's choice of language and, often, the consequences they bestow upon their characters.
In this story, we encounter a married woman and a married man taking advantage of a storm to consummate a passion that predates their marriages. Essentially, then, Chopin presents to us an act of adultery. We might expect her tone to be critical, then, but in fact the opposite is true. At the end of the story, Alce, the man involved, tells his wife that she should feel free to stay away with the children until their health has improved; there is a clear implication that the affair may well continue. But there is no punishment threatening—"everyone was happy." Chopin goes some way towards explaining this tone when she notes that Alce's wife, Clarisse, feels a "pleasant liberty" at the idea of being allowed to be away from her husband; her "conjugal life" with him is not something she wants to be obligated to continue. Meanwhile, Calixta does want to be intimately involved with Alce, even though they aren't married.
Chopin's tone is sympathetic to the fact that these women are being forced by society to live lives outside of what they would strictly prefer, and she is sympathetic too about all the characters' attempts to snatch happiness where they can, even if it may be construed as immoral.