The rumors were focused on people from the Roma ethnic minority, and police arrested 20 people after a number of attacks on the community, a police source told AFP.
In a statement Tuesday, Roma advocacy group La Voix des Rroms said the racist stereotype of a Roma child-thief has been around in France since the Middle Ages.
The group likened anti-Roma aggression to the massacre of the Rohingya in Myanmar, and called on people to form citizen protection groups to guard those whose lives are in danger.
CNN has contacted the group for further comment.
More violence took place on Monday in Bobigny and Clichy-sous-Bois, disadvantaged suburbs northeast of Paris, the source told AFP. There were no reports of injuries in that unrest.
The agency said the rumors appeared to originate from Facebook and Snapchat.
The attacks are "unacceptable," AFP reported government spokesman Benjamin Griveaux as saying. The incidents provided further evidence of "the absolute need to fight 'fake news,'" he added.
"Spreading such rumors in a highly organized and viral way on social media results in violence (and) the stigmatization of a community," he said.
