The uncle, a 28-year-old Togolese man, was sentenced to 14 years for raping his niece in the guise of "chasing out an evil spirit", as well as for assaults against the girl's two older sisters.
The victims' mother, 41, got seven years for complicity as she had even supplied the condoms used in the crime.
"She more or less delivered her daughter to the rapist," the prosecutor said.
The rapes took place between 2010 and 2011 in voodoo sessions organised by the man and his sister-in-law.
During these sessions, the man would wash the girls' genital areas, and cut their hands and legs before applying a purportedly magical black powder to the wounds.
The man was arrested in February 2011 after his last rape.
He claims that he is unaware of the rapes inflicted on his niece.
For the victim's lawyer, Daniel Merchat, "this denial is the second rape. It is a rape of the soul."
The prosecutor also said: "The voodoo belief that was cited is just window dressing," adding that the man "does not suffer from any mental illness... he
is completely responsible for his acts."
Cases of voodoo exorcisms come up from time to time in France, which has a large African community. Four men were recently sentenced for holding a young
woman captive and torturing her as they believed she was possessed.