Although Kate Chopin does not directly state that the story is set in the pre-Civil War South, several details from the story support this setting, such as the story's theme and the inclusion of plantations, slaves and slave owners, and French vernacular.
The story's themes of the oppression of women, male hypocrisy, and prejudice relate directly to the South before the Civil War. Desiree fortunately gets to marry for love, but because of the time period, even love is not enough for her husband to overlook his and others' prejudice toward a possibly mulatto wife. Similarly, Desiree has no choice but to leave her husband's home with their baby because men dominated her society, leaving her powerless. She cannot simply ease into single motherhood; instead, she has to write her mother to see if she can come back home. As a 19th-century woman, her whole life is dependent upon her husband's decisions.
The story's time setting also plays a huge role in Armand's actions. Because he is a slaveowner, he must set a precedent with his slaves in order for them to "obey" him, and decides to expel Desiree and the baby from the home so that no one challenges his authority (if he is married to a mixed woman).
Finally, the story's setting in the French part of Louisiana makes Armand's heritage and his lack of knowledge about it believable. For his mother to have lived in a more forward-thinking France during this time period is not far-fetched, and Armand would have been brought up thinking that his French mother simply preferred Paris to Louisiana.