Emmanuel Macron called for the Ligue de Football Professionnel (LFP) and fans to work together after a spate of domestic matches were marred by homophobia.
Ligue 1 games in Nice and Metz were paused in the space of a week last month after discriminatory banners were seen in the crowd.
A second-tier encounter between Nancy and Le Mans was the first to be stopped earlier in August as match officials acted on new instructions to intervene in the event of homophobic chanting or displays.
French Football Federation president Noel Le Graet believes referees have been wrong to halt matches, while sports minister Roxana Maracineanu backed the LFP's attempts to stamp out discrimination.
Macron, the president of France, wants to see authorities and fans work together.
"It's a question of discernment," he said on Tuesday.
"It's the role of the referee, it's the role of the league with the clubs. The LFP and the clubs have to take their responsibilities, talk to the fans, not edit a fixed rule."
It comes after Le Graet criticised referees for stopping matches, saying homophobia was a society-wide issue.
"I would not stop the matches," he told France Info.
"It's a mistake, totally, because I don't want to be held hostage to homophobia. I would stop a match for racist abuse, that's clear, or for security reasons.
"We're going to make sure the banners disappear, there is security to make sure that happens, but stopping matches is something else.
"It's not football but society in general that has to think about the problem, at school and in companies, everywhere."
Addressing the fans responsible, Le Graet said: "Do not come to the stadium with banners, it's as simple as that.
"You can support your team, but [homophobia is] absolutely wrong morally."