Raphael Varane says he has "damaged his body" because of the continued impact of heading the ball.
Defender Varane, now at Manchester United, says he once finished a France World Cup game in 2014 on "autopilot" after playing on with concussion.
He has called for greater protection and better awareness of the issue.
"My seven-year-old son plays football and I advise him not to head the ball. For me, that's essential," Varane told L'Equipe.
"Even if it doesn't cause any immediate trauma, we know that in the long term, repeated shocks can have harmful effects.