Aya Garde said in China, Russia and African countries such things are common but it is the first time he has heard of it happening in France.
The remarks by Macron are problematic in terms of freedom of expression, he said, adding that France has turned into a country where human rights were restricted.
"This is not good news," he said.
A prominent media figure, who did not want to be identified because of security concerns, stressed that freedom of expression is a fundamental right that should not be curbed and such a move would violate France's essential values.
Leonie Salvo, a social media user, said criticism should not be seen as opposition to the French state.
"We have no intention to destroy France," he said.
Another user, Magali Davrou, argued that social media can be limited in emergencies but it should not be turned into a bigger move to restrict freedom of expression.
Protests started last week when a police officer shot dead Nahel M. during a traffic check in the Parisian suburb of Nanterre after he allegedly ignored orders to stop.
The officer who fired the shot faces a formal investigation for voluntary homicide and has been placed under preliminary detention.
After starting in Nanterre, protests quickly spread to other cities, including Lyon, Toulouse, Lille, and Marseille.
Tensions rose following clashes between the police and protesters, before losing steam this week.
Police arrested 20 more people overnight in nationwide protests, while 55 vehicles and buildings were set on fire, and 81 fires were recorded on the public ways, mostly in trash bins, according to Interior Ministry figures provided to the Le Figaro newspaper.