French President Emmanuel Macron came under fire on Thursday after his office briefly suspended one of his aides for beating a May Day protester and posing as a police officer, but did not inform law enforcement authorities.

Critics of Macron said the incident reinforced perceptions of a lofty, out-of-touch president, following controversies over government spending on official crockery, a swimming pool built at a presidential retreat, and cutting remarks by the president about the costs of welfare.

A video from a May Day rally this year, released by Le Monde newspaper on Wednesday, showed a man wearing a police helmet and identification tag dragging a woman away and then beating a demonstrator. He was later recognised as a member of the French presidency staff.

"The staff member, Alexandre Benalla, had been given permission to witness the demonstrations only as an observer," presidential spokesman Bruno Roger-Petit said in a video statement.

"Clearly, he went beyond this...He was immediately summoned by the president's chief of staff and given a 15-day suspension. This came as punishment for unacceptable behaviour."

On a trip to southwestern France on Thursday, Macron declined to answer questions from reporters on the subject, saying only in a video posted by a Le Figaro reporter: "I didn't come here to see you. I came to see Mr Mayor."

The Paris prosecutor, which was unaware of the matter before Thursday, launched a preliminary investigation against Benalla on suspicion of violence, usurping the function of a police officer and using signs reserved for public authorities.

Later the speaker of the lower house of parliament, Francois de Rugy, announced a parliamentary inquiry into the case.

Opposition parties condemned the presidency's handling of the matter, arguing the punishment was too lenient and that the incident should have been referred promptly to judicial authorities.

"This video is shocking. Today we have the feeling that in Macron's entourage one is above the law," Laurent Wauquiez, president of the conservative Republicains, told Europe 1 radio.

Far-left leader Jean-Luc Melenchon told reporters: "If we accept that anybody can be a policeman alongside the police then we no longer have the rule of law. This man is the eyes and ears of the prince (Macron)."

Some lawmakers in Macron's centrist party also called for Benalla to be dismissed. Prime Minister Edouard Philippe, who denounced "shocking images" in the video, said it was now up to the courts to decide.

Labour unions hold demonstrations every year on May 1 in France and clashes with police are not uncommon.

After the 15-day suspension, Benalla was brought back into the president's immediate entourage. He appears in many Reuters photos alongside Macron during public events.

Benalla also helped to organise festivities when France's World Cup champion soccer team came home earlier this week and is seen next to the team bus.

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