Third person omniscient is perfect for this story. Of the five sections, each comes at us from a different character or characters' point of view. We emerge from the story knowing exactly how everyone feels once the storm has passed.
Sounds easy, right? New section, new narrator(s). Well, that's kind of true. The thing about Chopin's narration is that it seems simple, but it's actually kind of complicated. Let's take a look:
Oh! she remembered; for in Assumption he had kissed her and kissed and kissed her; until his senses would well nigh fail, and to save her he would resort to a desperate flight. If she was not an immaculate dove in those days, she was still inviolate; a passionate creature whose very defenselessness had made her defense, against which his honor forbade him to prevail. Now – well, now – her lips seemed in a manner free to be tasted, as well as her round, white throat and her whiter breasts. (2.18)
Interesting stuff going on with point of view here. Whose point of view is this passage from, Calixta's or Alcée's? We hear from both of them in just one paragraph: "she remembered," "his honor forbade him," etc. In the present, we feel both of them share their memory and respond to it. In the past we relive how she was "inviolate," how he would "resort to a desperate flight." Back in the present, the passage ends by leaving the specific point of view ambiguous through the use of passive voice: "her lips seemed in a manner free to be tasted." Who's thinking this part? Does it feel to Alcée like the lips are free, or does Calixta feel like she's presenting them that way? The benefit of third person point of view here is the way it enables the narrative to move back and forth between the two characters so quickly, creating a more three-dimensional image of what this present moment is like.