Regionalism has to do with using the details of a particular place or culture as identifying features of the text. Naturalism is a literary movement that discounts emotion and spirit and emphasizes an objective, "scientific" approach to representing reality. "Désirée's Baby" is an example of both.
As regionalist literature, the story relies on many details about French culture in pre–Civil War Louisiana. These include the complex social hierarchy in which the Valmonde and Aubigny families exist, but also other small details, such as how they speak French in the home or the tradition of the corbeille, which is a set of clothing and personal items given by the groom to the bride.
The most important regional detail, however, is the complex racial hierarchy that existed in Louisiana at the time. Aubigny's conclusion that Désirée is "not white" because her baby has darker features goes to show how irrational racial attitudes were at the time and how Désirée's status as an adoptive daughter makes her a scapegoat for Aubigny's own racial impurity.
As a naturalist text, the story is concerned with observing the "rules" of Désirée's society and what happens to her and her baby as a result. None of the characters have much interior complexity; the things they do are in reaction to external stimuli. In this regard, we can see that the society is both racist and sexist; when Désiree is named "not white" by her husband, she loses all status. Her return to her mother suggests a kind of matriarchal alternative to Aubigny's authoritarianism.