The general frame of a short story is understood to hang around a central conflict or problem that the characters must deal with and react to. In this story, set in the antebellum Southern US, there are various conflicts, both internal and external; but the chief instigating factor is that Désirée gives birth to a child who is evidently "not white."

This, of course, sparks various other points of conflict for the characters. Because of the context in which the story is set, the idea that "slavery" might taint their family history is difficult for either Désirée or Armand to contemplate. Armand insists that it is Désirée's fault that the child is not white; he suggests that she has lied to him. Désirée, meanwhile, is so ashamed of this and so distraught by her husband's rejection that she leaves her husband and walks into the bayou with their child, presumably to kill both herself and the baby.

This is evidence of a strong conflict between both of these people and the society in which they live. The racism of their society means that they find it impossible to love either each other or their baby in the way they had before they believed that there was any likelihood that they had Black heritage.

Of course, at the end of the story, it is revealed that Armand, not Désirée, was the parent with Black heritage. Whether Armand knew this before he rejected Désirée is unknown: if he already knew, he likely felt so ashamed that he blamed Désirée instead, causing her to commit suicide.