The last line reflects not only the short story's racial themes but also the theme of a mother's love and how that love can instinctively affect the decisions you make later on in life.
The racial themes are apparent first in the characters need to hide any kind of evidence that they have black blood. Even if people in the South knew you had a distant relative who was black, they would still view you as inferior to the white race.
This is the reason the author suggests people didn't take to the beautiful Désirée. People didn't know her origins. The Valmondes found her as a baby, and although they did their best to quash the rumors, people didn't trust that she was purely white.
It is therefore interesting that Armand is not only bowled over by her but doesn't care about her origins. As the author states, “he was reminded that she was nameless. What did it matter about a name when he could give her one of the oldest and proudest in Louisiana?” Rather than go by his thoughts, he does what the author says all his family did and goes by his instincts.
The origins of his own instincts come clear at the end when the author tells the reader that his mother had Negro blood. In that regard, he is attracted to Désirée because, like him, she has a past that may or may not be acceptable to their people. Like his mother, he feels that she would love him no matter what.
Unfortunately for Armand, he is the one who can't accept that he has Negro blood. Whether he means to or not, he uses Désirée and her unknown past as a way to keep his standing in society. It seems that the fear of being found that you have black blood is greater than the fear of spending the rest of your life alone.