French President Emmanuel Macron leaves his house with his deputy chief of staff Alexandre Benalla (L) on the eve of the second round of the French parliamentary elections on June 17, 2017, in Le Touquet-Paris-Plage, France.

A scandal involving the security guard of Emmanuel Macron has fast become the biggest crisis of the president's short spell as leader.

During a protest on May 1 his 26-year-old security aide Alexandre Benalla was captured on video hitting a male protester and violently manhandling another woman.

Bennalla was wearing a police visor and helmet but was only supposed to be observing the police in action. A few days after the incident Macron suspended Benalla, but the security official was not sacked until July 20, a few days after being identified by the newspaper Le Monde.

Macron has drawn criticism by remaining largely silent over the matter but added fuel to the fire Tuesday by telling his own ministers at a closed-door event that his rivals "could come and get me if they dare."

A political analyst at Sciences Po, Thomas Guenole, told CNBC Thursday that such a statement showed Macron is behaving "like a child-king, and not like a statesman."

Guenole added that Macron's cultivated image of a brave and strong leader had been damaged by his refusal to publicly confront the press or rival politicians. The analyst said the scandal could prove very costly.

"This 'BenallaGate' is a French Watergate. Because just like the U.S. one, the problem is not the crime but the cover-up. The French people saw lieutenants and ministers of Macron lie repeatedly," he said via email.