In Kate Chopin's short story, the storm itself only influences the characters' physical convergence, because Alcée has to find refuge inside Calixta's home as the storm approaches. Initially, Alcée does not intend to go inside of Calixta's house, but the intensity of the storm forces him to seek shelter.
The storm is a blatant analogy for the two former lovers' increasing passion. As the storm intensifies, so does their sexual desire for each other. Even if the storm were not featured in the narrative, it is evident that Alcée and Calixta would have initiated a short-term affair at some point. In this regard, the storm—or, rather, the chain of events that the storm causes—does not excuse their respective infidelity.
In the end, both characters decide to stay in their respective marriages and seem happy with the experience. They show no remorse, which appears to be Chopin's message: that passion and love can remain innocent even if infidelity is involved. The author wants to convey that morality is subjective and a social construct.