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.
Mr Zecler said he was also subjected to racist abuse during the five minute beating.
He was detained and charged with violence and resisting arrest, but prosecutors threw the charges out and instead opened an investigation against the officers.
As he arrived at police headquarters on Thursday with his lawyer to file a complaint, Mr Zecler told reporters: “People who should have been protecting me attacked me. I did nothing to deserve this. I just want these three people to be punished according to the law.”
Paris Mayor Anne Hidalgo said she was “profoundly shocked” by the “intolerable act”.
Earlier this week, Mr Darmanin also ordered police to provide a full report after they violently dismantled a makeshift migrant camp in the capital, clashing with migrants and activists.
He tweeted that some of the scenes were “shocking”.
Meanwhile, the French government is pressing ahead with its controversial security bill, which opponents say could undermine the media’s ability to scrutinise police behaviour.
Article 24 of the bill makes it a criminal offence to post images of police or soldiers on social media which are deemed to target them as individuals.
Critics of the legislation say that without such images, none of the incidents which took place over the past week would have come to light.
The government argues that the new bill does not jeopardise the rights of the media and ordinary citizens to report police abuses.
But in the face of criticism the government added an amendment, specifying that Article 24 “will only target the dissemination of images clearly aimed at harming a police officer’s or soldier’s physical or psychological integrity”.
People found guilty could be punished by a year in prison or a fine of up to €45,000 (£40,000).