Social media and other websites will have just one hour to delete offending content under a new law passed by France's parliament, reports BBC News.
The one-hour deadline applies to content that French authorities consider to be related to terrorism or child sexual abuse.
Failing to act could result in fines of up to 4% of global revenue - billions of euros for the largest online firms.
But critics say the new law could restrict freedom of expression.
The new rules apply to all websites, whether large or small. But there are concerns that only internet giants such as Facebook and Google actually have the resources to remove content as quickly as required.
Digital rights group La Quadrature du Net said the requirement to take down content that the police considered "terrorism" in just one hour was impractical.
"If the site does not censor the content, for example because the report is sent on a weekend or overnight, the police can require [the whole site] to be blocked everywhere in France by internet service providers," it said.
It said the power to decide what should be removed should not lie with the police but with judges.
France's new law reflects one proposed at the European Union level, where law-makers last year suggested a one-hour deadline for the removal of content.
France pushed ahead with its own version of the law despite the concerns in Europe.
Under the new French law, content judged to be illegal - but not relating to terrorism or child sexual abuse - will have to be taken down within 24 hours of notification.
That includes posts inciting hatred, violence, racism, and sexual harassment.
Failure to remove content could attract a fine of up to 1.25 million euros.