The story, set in the south in the middle of a torrential downpour, is all-important in being the catalyst for the action that occurs. First of all, if there was no storm, Bobinot and Bibi would have been home a lot sooner than they were, and the opportunity for Calixta and Alcee to act would have been cut short. Secondly, if it weren't for the storm, who knows if Alcee would have even stopped at the house at all. Then, if it weren't for the storm, he at least probably wouldn't have come inside. He planned, originally, to stay outside on the porch, but, as Chopin writes,
"it was soon apparent that he might as well have been out in the open: the water beat in upon the boards in driving sheets, and he went inside, closing the door after him."
So, even if it had been a light shower or storm, he could have stayed outside, and they might not have succombed. But, the rain is intense, driving in at a sideways slant, so he has to come in.
Then, note the arrangement of the house. As soon as he steps in, he can see into her bedroom. Chopin probably planned that on purpose; seeing that room suggested things to both of their minds that further tempted them both. The lightning and thunder then drove them into each other's arms, where the temptation was too much to bear.
The storm was the critical factor in this story, and the floor plan of Calixta's house. If any of those had changed, they probably wouldn't have acted the way that they did, that day. Chopin does hint, at the end of the story though, that Calixta and Alcee find great happiness in each other, and even become better spouses because of their tryst; so, maybe eventually they would have each strayed in their own way, since it seems they weren't happy in their stations. But for the events of this story, the storm and setting were crucial. I hope that helped; good luck!