Why do all the American characters in "Desiree's Baby" have French names?
The story "Desiree's Baby" is set on a plantation in Louisiana. That area was colonized by the French in the 17th century. That is why even today many placenames and people's surnames sound French. The area was briefly controlled by Spain before being sold to the United States in what is called the Louisiana Purchase.
Two different offshoots of French are spoken by the people of this area, especially in the era in which Chopin's story is set. One variety is Creole, a mixture of French and Spanish with a little English thrown in. This is what Desiree and Armand would have spoken. The other type of French, Cajun, is derived from the Acadians, a group of French people who had originally settled in Nova Scotia but who fled the cold climate for warmer Lousiana. The Acadians were a "peasant," or farmer, class. The Creoles were a landowner class and strove to stay close to their French roots. Many families sent their children to France for education.
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Kate Chopin was from Louisana, a place the French originally settled and which still has a strong French influence. French is still spoken in many parts of the state and French names are common. Since Chopin's setting for the story is in the Cajun ( French speaking) part of Louisana, the names are French to reflect that heritage.