President Emmanuel Macron says footage of three police officers beating up a black music producer in Paris is "unacceptable" and "shameful".
He demanded quick proposals from the government aimed at rebuilding trust between police and citizens.
France should never "resign itself to violence" or "let hatred or racism prosper", he said.
The three officers identified in the video beating Michel Zecler have been suspended and are under investigation.
They were questioned in police custody on Friday.
Interior minister Gérald Darmanin has told French television that he will press for the officers' dismissal, saying they had "soiled the uniform of the republic".
The incident has led to fresh scrutiny of the security forces.
Stars of the French World Cup football team are among a number of public figures who have spoken of their anger after the footage captured in the French capital was made public.
Earlier on Friday, French media reported that a presidential official had described Mr Macron as being visibly upset by the incident.
In a series of tweets Mr Macron said proposals were also needed to fight more effectively against all types of discrimination.
"Those who apply the law must respect the law. I will never accept that the gratuitous violence of some stains the professionalism of the men and women who work courageously to protect us in our daily lives," he said.
On Thursday, French football star Kylian Mbappé, who is black, joined national teammates and fellow athletes in condemning the latest incident.
"Unbearable video, unacceptable violence. Say no to racism," he wrote on Twitter next to a picture of the bloodied face of the injured producer.
The security camera video was published on Thursday by the online news site Loopsider. It shows three officers kicking, punching and using their truncheons on the man after he entered his studio. Loopsider said he had initially been stopped for not wearing a mask.