In the footage recorded secretly, the man tells the women: “Terrorists are Muslims and all Muslims are terrorists.”
The incident took place at Le Cenacle restaurant in Tremblay-en-France on Saturday night.
On Sunday, the man apologised to a group of protesters who had gathered outside.
He said he had “got out of hand” due to the current tensions around the issue of wearing burkinis on French beaches, but also because he had a friend who had died at the Bataclan concert centre attack last November, Le Parisien reported.
The local prosecutors’ office told the paper that it had opened an investigation into racial discrimination.
Government Minister Laurence Rossignol said that she had asked Dilcra, a government anti-racism body, to investigate, describing the behaviour as “intolerable”.
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French anti-Islamophobia organisation CCIF said that “following the umpteenth Islamophobic incident which… led to the humiliation of two young Muslim women” its director would be speaking outside the local mosque on Sunday evening.
The CCIF, which says it’s offering legal and psychological support to the two young women, appealed for no protests outside the restaurant itself.