- 14 September 2016
- From the section Europe
He said it was unpatriotic because it did not come from an official list of French Christian names.
Ms Dati, a former justice minister, said the comments were "pathological".
Zemmour appeared on French television channel LCI on Monday, demanding the return of a law restricting the names children are given.
The law was abolished in 1993, 200 years after it was brought in by Napoleon Bonaparte.
Five countries which regulate baby namesIceland: Parents can choose from an approved list of 1,853 female and 1,712 male names, with those who want to venture outside the norm facing a special committee which will approve the choice should it meet certain criteria - including not embarrassing the child in question
Portugal: Those looking for inspiration can turn to an 80-page list which includes some 2,600 banned names, according to the Portuguese-American Journal
Saudi Arabia: The kingdom banned 50 names in 2015, including Alice, Elaine and Lauren - all considered too Western by authorities.
New Zealand: The task of approving baby names falls to the Department of Internal Affairs, which releases a list of its top "most rejected" each year - with 2015's winner being "Messiah"
Malaysia: As well as banning parents from calling babies names like Hitler, the National Registration Department has prohibited naming children after animals, insects, fruit, vegetables or colours since 2006
Zemmour - who also told the channel he felt National Front leader Marine Le Pen was not far enough to the right - said non-Christian names like Zohra, and that of football legend Zinedine Zidane, made their bearers "less French" than himself.
He also admitted to confronting Ms Dati, who is of North African origin, over her choice of name to her face.
"She called her daughter Zohra," he said. "I find it outrageous and I told her."
He added: "I consider that by giving Muslim first names, you are refusing to accept the history of France."
Ms Dati, who was justice minister under ex-President Nicolas Sarkozy, was raised in a Muslim household but was partially educated at a private Catholic convent school. She has spoken previously of how she considers herself first a "daughter of France".
"Do you find it scandalous to give your mother's name to your children?" she asked, in a vigorous defence of her choice of name.
"I loved my mother. I have a little girl, and I called her after my mother. Like millions of French people do every day."
Read more: http://www.bbc.com/news/world-europe-37359437