"We need to think about how young people use social networks, in the family, at school, the interdictions there should be ... and when things get out of hand, we may have to regulate them or cut them off," Macron told a meeting of more than 250 mayors, whose municipalities were hit by the violence.
Elysee officials and government ministers responded by insisting the president was not threatening a "general blackout" but instead the "occasional and temporary" suspension of platforms.
The president's comments came as ministers blamed young people using social media such as Snapchat and TikTok for organising and encouraging rioting and violence after the shooting death of a teenager during a police traffic stop in a Paris suburb last week.
Critics said considering such measures would put France alongside authoritarian countries such as China, Russia, Iran and North Korea.
Government spokesperson Olivier Veran said a cross-party committee to look at a modification of a law on cybersecurity currently going through parliament would be set up.
Veran said the government had made a "firm request" to social media platforms to take down materials encouraging violence as quickly as possible and remove the anonymity of those possibly breaking the law.
A young person should know he cannot sit behind his screen and write, organise or do whatever he wants. Anonymity in terms of offences doesn't exist. You have to understand this can have consequences and the consequences can lead to punishment," Veran said. Asked if it meant suspending social media, the Veran added: "It could be something like suspending a function, such as geolocalisation."