Alexandre Benalla, an assistant to President Emmanuel Macron’s chief of staff, was filmed targeting a woman and a man during May Day protests.
He was caught on video by a student activist and left the scene once challenged on camera.
He was identified from the video by French newspaper Le Monde.
On Thursday, it emerged he was accompanied on the day by a reserve policeman and employee of Mr Macron’s political party, Vincent Crase.
France’s Interior Minister Gerard Collomb said he had ordered an investigation by the country’s national police inspectorate.
“These two people had no legal right to intervene,” he said.
The incident took place in a popular tourist spot at Place de la Contrescarpe in the fifth district of Paris, where about 100 people had gathered on 1 May.
The original video, posted on social media by 21-year-old Taha Bouhafs, shows a man in a police helmet who is not in uniform joining CRS riot police after clashes erupted.
He grabs a woman by the neck, charging her down the street, before both disappear off-camera.
Shortly afterwards he returns to the scene, attacking another protester who had been carried a short distance by police before being left alone on the ground.
The man in the helmet, since identified as Mr Benalla, can be seen grabbing the young protester around the neck, hitting him in the head and apparently stamping on his stomach when he falls to the ground.
Mr Crase is also seen in the fray, holding on to the same protester on the ground before Mr Benalla grabs him.
Riot police do not appear to intervene.
Speaking to French radio on Thursday, activist Taha Bouhafs said that protesters had been “quietly settled” on the square before he recorded his video. “The man on the ground was harmless and begged Benalla to stop,” Mr Bouhafs said. “There is no explanation for this outburst of violence.”
A presidential spokesman said Mr Benalla had been given permission to attend the disturbance as an observer on his day off. Other photographs show him wearing a police armband.
The Élysée palace later revealed that Vincent Crase, who was seen with Mr Benalla at the scene, had been given the same permission to attend.
A reserve police officer, he started a private security company with Mr Banella, and French media report that the pair are close friends.
Mr Crase has been suspended by En Marche.
Who is Alexandre Benalla?
Mr Benalla’s main duty is to arrange security for the president’s engagements.
Before he joined the presidential staff he had the role of head of security during Mr Macron’s election campaign in 2017.
In that role, he was a constant companion to the future president, and archive photographs show the two men together at many high-profile public events.
But Richard Ferrand, a senior member of Mr Macron’s party, sought to downplay the importance of Mr Benalla’s role.
“This is not a close aide, this is someone who was in charge particularly during the presidential campaign and then he joined the Elysée staff,” he told French TV.
President Macron, asked if he had confidence in his bodyguard on Wednesday night, pointed to a member of his entourage. “My bodyguard’s over there,” he said.
Formerly an employee of a private security firm, Mr Benalla had worked with other French politicians in the past – including leading Socialist Martine Aubry and Mr Macron’s predecessor in the Elysée, François Hollande.
In 2012, he was hired as a driver for Industry Minister Arnaud Montebourg.
Mr Montebourg told Le Monde that Mr Benalla was fired for misconduct after causing a car accident in the minister’s presence and wanting to flee the scene.
What has the reaction been?
Elysée palace spokesman Bruno Roger-Petit said Mr Benalla had been suspended for two weeks without pay from 4 to 19 May, a punishment described as the heaviest so far meted out to a head of mission working at the presidential office.
He had also been moved out of his role of organising security for the president’s visits.
However, French TV reported that Mr Benalla had handled security for two key events this month, including the parade of the World Cup-winning France football team along the Champs-Elysées.
Paris prosecutors announced on Thursday they were opening a preliminary investigation into the alleged assault by Mr Benalla.
Possible charges include violence by a public official, pretending to be a policeman and the illegal use of police insignia.
Interior Minister Gerard Collomb announced that an investigation into how police observers were supervised had been ordered – and to see if all rules had been followed in the case of Mr Benalla and Mr Crase.
Prime Minister Edouard Phillippe added his voice to the widespread criticism, calling the incident “particularly shocking”.
He said the behaviour “cast doubt on the integrity and exemplarity of our police” – but added the case “is now in the hands of justice” after prosecutors announced their preliminary investigation.