Violence at rallies has prompted a counter-demonstration by groups calling themselves the "red scarves" and "blue vests".
French police are investigating how a prominent yellow vest protester suffered a dramatic eye injury in Paris, as well as other protest-related injuries.
Violence by protesters and the sometimes-aggressive police response have prompted a national debate since the anti-government movement kicked off two months ago.
A counter-demonstration is planned on Sunday in Paris by groups calling themselves the "red scarves" and "blue vests" to protest the violence.
Elena Casas has more from Paris.
Paris police said on Sunday they are investigating the eye injury of protester Jerome Rodrigues, among other protest injuries.
Video images show Rodrigues collapsed on the ground Saturday near the Bastille monument in Paris, where protesters throwing projectiles clashed with police seeking to disperse them.
The movement sees French President Emmanuel Macron's government as favouring the wealthy. Most of its actions are peaceful.