The child, who cannot be named for legal reasons, "admitted the facts" in court, the source told AFP on condition of anonymity.
The incident took place yesterday at the Anatole-France primary school in a poor, high crime area of the city.
The 11-year-old stabbed a 12-year-old in the stomach in front of their classmates, said a police source, adding that the victim had allegedly tried to extort money from him.
The child was temporarily placed with a foster family Under French law children between the ages of 10 and 13 can be held criminally responsible, but will not be imprisoned.
"These two students were not known for being violent. They dealt with matters among themselves and the only response was violence. That means the community failed and that makes me angry," said communist local mayor Michele Picard.