A source close to the inquiry also said that three officers, including two high-ranking officials, have also been suspended on suspicion of providing the footage to Benalla.
The man was identified as Alexandre Bennala.
The Elysee Palace said Alexandre Benalla would be dismissed after "new elements" emerged in the case, namely that he is suspected of unlawfully receiving police surveillance footage in a bid to prove his innocence.
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.
Macron has not yet officially reacted to the scandal. However, he maintained his office at the presidential palace.
It was unclear why the young man under attack, who wasn't detained, was singled out by police before Benalla intervened.
'The day after the demonstration, I was informed by a colleague that Mr Benalla had been recognised in the field as being involved in law enforcement operations, and I saw the videos.
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A video of the May 1 event in Paris shows Benalla, in a helmet with police markings and surrounded by riot police, brutally dragging away a woman from a demonstration and then repeatedly beating a young man on the ground.
Opposition parties say the punishment is too lenient.
"Clearly, he went beyond this ... he was immediately summoned by the president's chief of staff and given a 15-day suspension".
When the 21-year-old saw Benalla grab a woman by the neck and attack an already "neutralized" male protester, he made a decision to confront him on camera.
Prime Minister Edouard Philippe, who denounced the "shocking images" in the video, said it was up to courts to decide on the matter.
But in another potentially damaging twist, the BFM news channel reported that Benalla had been back on duty doing security work this week, travelling on the bus carrying France's World Cup-winning football team down the Champs Elysees for a victory parade. After hours of debate in the lower house on Thursday, lawmakers agreed to launch a parliamentary inquiry into the case.
"I'm surprised he hasn't resigned", said conservative politician Jean-Christophe Lagarde, adding that if Mr Benalla did not resign himself, the President should remove him or risk the drama becoming "an affair of state".