Yes, he had a brother Paul…

[Young Man Sketching. William Bruce Ellis Ranken]

• Louis’ brother: “He had the smoothest skin and the largest blue eyes. He was robust, not thin as I am now and was then” (IWTV) Not sure whether it’s canon or fanon but Paul was supposedly blond. He was 15 when he died, right after an argument in which Louis had laughed at him, had not believed him, and so, felt responsible for Paul’s death.

• Louis’ sister: Unnamed (it’s fanon that her name is Henriette “Minette“ de Pointe du Lac), she played the harpsichord. After Paul died “My sister went to bed rather than face the funeral… People in society asked my sister offensive questions about the whole incident, and she became an hysteric. She wasn’t really an hysteric. She simply thought she ought to react that way, so she did…  I did come to know my sister, forbidding her the plantation for the city life which she so needed in order to know her own time of life and her own beauty and come to marry, not brood for our lost brother or my going away or become a nursemaid for our mother.”
• Louis’ mother: Unnamed (it’s fanon that her name is

  Paulette de Pointe du Lac) Louis didn’t seem to have a great relationship with his mother. When Paul died, “my mother told everyone in the parish that something horrible had happened in my room which I would not reveal; and even the police questioned me, on the word of my own mother.” 

• Louis’ father: Unnamed (it’s fanon that his name is

  Aurestile Jean Michel Pointe du Lac) At the beginning of IWTV, Louis is 25, his father is dead and Louis “was head of the family and I had to defend [Paul] constantly from my mother and sister.” Defend him from their trying to get him to go out and have fun; but Paul was committed to the Bible.