A man who harassed a woman on a Paris street and then hit her in the face when she told him to stop was caught on video, provoking an uproar in France.

Marie Laguerre, a 22-year-old student, shared surveillance video from a café that showed a man, whom she did not know, angrily throwing an ashtray at her and later assaulting her after she told him to stop harassing her.

It's now been seen by over a million people and has been picked up by news agencies across Europe.

"The impact that a simple video can have…" Laguerre said in a post on her Facebook page.

"Hoping it'll make things move for all women who suffer from harassment and sexist violence on a daily basis."

Laguerre told a French radio station she was walking home on the street outside the café, in the city's northeast, when a man made degrading comments and "noises with sexual connotations."

As she walked away, she told him to "shut up."

The man threw an ashtray at her, then reversed direction and followed her, hurling insults.

She stood her ground. "I wasn't going to apologize," she said.

"He hit me in the face, on the street, in the middle of the day, in front of dozens of witnesses," Laguerre said on Facebook.

People sitting in the outdoor café jumped to their feet and appeared to remonstrate with the man, who then left the area.

Laguerre said she went home, but after thinking about it returned to the café to talk to witnesses and complain to police. The café owner gave her the footage.

Video shows woman being followed and struck when she asks a man not to harass her

Her post has provoke widespread reaction, including many comments asking why the bystanders did so little.

Laguerre later added a postscript.

"To all those who say that witnesses have not reacted enough: everything happened very quickly and they did not have time to understand the situation. The attacker was dangerous. After the assault, I came back and witnesses were of great support," she wrote.

She said his behaviour was "unacceptable" but nevertheless common.

The French equalities minister Marlène Schiappa responded to the July 24 attack, saying she was "outraged… but not surprised, unfortunately."

France plans to introduce on-the-spot fines for harassment in public, with the law to take effect this fall. President Emmanuel Macron said the aim is to ensure "women are not afraid to be outside."

There will be fines for "degrading or humiliating comments" or hostile and offensive "sexual or sexist" behaviour toward a person in a public place.