The boy kicked the girl, 10, once in the chest after blaming her for a crush in the canteen queue at the school in the suburbs of the southwestern town of Angouleme, prosecutor Nicolas Jacquet told AFP.
The girl collapsed immediately and emergency services pronounced her dead after giving her heart massage for 45 minutes.
The prosecutor has ordered an autopsy on the dead girl and called for psychological help to be provided to her family and to witnesses.
Local health and safety official Cedric Esson told AFP the investigation was “based on the hypothesis of a complete accident” after the prosecutor said the kick appeared to have been a “reflex gesture.”
The two children were in the same class, and teachers described the boy as “calm” and with no disciplinary problems.
Esson said police would interview the boy, who is being looked after by psychologists, “when he’s able to be interviewed.”
Mayor Francois Nebout said teachers and the girl’s family were in shock, in particular a younger brother who was in the canteen at the time.