The character La Blanche in Kate Chopin's "Désirée's Baby" is important throughout the story. The name itself is significant, as has been said, because it literally means "the white." This entire story focuses on race, so the name is meant to indicate that this slave, whose cabin is near the main house, is one who could, given the right circumstances, pass for white. This ability to pass is extremely important for Armand, whom I would argue, is aware of his mixed heritage.
In the story, La Blanche is the mother of the "little quadroon" boy fanning the baby. It is in her looking back and forth between La Blanche's boy and her own son that Désirée first becomes aware of what so many others have already noticed: her son and La Blanche's son are the same color—they are both mixed.
Hidden or mysterious identity his suggested throughout the story. Désirée is first found in the "shadow or a column" and is of unknown parentage. It is not surprising that the mixed child might be attributed to her "obscure origins." But a closer reading will reveal that it is Armand whose surroundings are secretive. The very description of L'Abri, the plantation, indicates obscurity with its "roof [that] came down steep and black like a cowl, reaching out beyond the wide galleries that encircled the yellow stuccoed house." A cowl is the hood of a monk's robe and obscures his face. This "cowl" is black and hangs over the "yellow" house like a dark secret. Note that the nursemaid, Zandrine, is also called "yellow," a color that indicates mixed heritage. So if a dark secret covers a house whose color indicates mixed race, it suggests that what is being covered is the family's mixed race.
Some have argued that Armand only learned that his quadroon child was a result of his own mixed race after the presumed death of his wife and baby, but I would argue that he knew all along and was hoping for a child that was white enough to pass—a child "as white as La Blanche." This knowledge would explain his rush to marry Désirée, whose shadowy ancestry could be used as an excuse should he father a child who was "not white." He could blame his wife, who, too, was "as white as La Blanche."
The fact that La Blanche lived so conveniently close to the main house, that Armand frequented her cabin, and that she had children might suggest that Armand was her son's father. Her son, a quadroon, is darker than La Blanche. Armand, as Désirée points out when Armand accuses her of being "not white," is also darker than Désirée, who Armand retorts, is "as white as La Blanche."
La Blanche, the whitest slave, represents a person of mixed race who is white enough to pass for white. Had her heritage been unknown, like Armand's and Desiree's, she could have passed for white.
But since the child did not pass, Armand was forced to blame his wife. He was forced to burn the last remaining trace of his own heritage, the letter from his mother. I find it difficult to argue that he was unaware of this letter, which he kept in the same drawer as his letters from Désirée. I also find it difficult to argue that he, who was eight years of age when his mother passed away, was unaware of his heritage, unless, she, too, was "as white as La Blanche," belonged "the race that is cursed with the brand of slavery."