The teenager, named William, was found dead by rescue personnel at 12:30 on Tuesday morning in the Upper Escaut canal, close to the Belgian border.
According to a preliminary investigation, the boy had lent two video games to a group of four other boys, who then threatened to throw them into the canal if he did not jump in first.
"He would have done anything to make friends," William's mother, Françoise Bachelet, 37, told the L'observateur du Valenciennois newspaper, adding that her son did not know how to swim.
The other adolescents watched him jump into the water, sink, resurface briefly and then disappear, she said.
The boys called emergency services, which quickly arrived on the scene. Around 30 personnel were on hand for the search-and-rescue operation, which included divers and canine teams. William's body was found about four hours later.
Three of the four young people were taken into custody and an investigation to determine the exact circumstances of the incident is ongoing.
A fourth boy, ten years old, was returned to his parents.