France’s political right celebrated the ban on the Muslim dress but the left argued it represented an affront to civil liberties.
Issues with the ban on the first day appeared limited.
“Things are going well this morning. There is no incident for the moment, we will continue all day to be vigilant so that the students understand the meaning of this rule,” said Prime Minister Elisabeth Borne, as she visited a school in northern France.
But she said there was a “certain number” of schools where girls arrived wearing an abaya.
“Some young girls agreed to remove it. For the others, we will have discussions with them and use educational approaches to explain that there is a law that is being applied,” Ms Borne said.
A law introduced in March 2004 banned “the wearing of signs or outfits by which students ostensibly show a religious affiliation” in schools.
This includes large crosses, Jewish kippas and Islamic headscarves.
Unlike headscarves and abayas – a long, baggy garment worn to comply with Islamic beliefs on modest dress – occupied a grey area and had faced no outright ban until now.
French Education Minister Gabriel Attal told RTL radio that the government identified 513 schools that could be affected by the ban.
He said work had been done before the start of the school year to see in which schools this could present a problem. Trained school inspectors would be placed in certain schools, he said.
There are about 45,000 schools in France, with 12 million pupils going back to school on Monday.
The hard-left has accused the government of centrist President Emmanuel Macron of using the abaya ban to compete with Marine Le Pen's far-right National Rally party.
Mr Attal said he was against imposing a ban on parents wearing clothes that had religious significance when they accompanied their children on school outings.
“There is a difference between what happens in school and what happens outside school. What matters to me is what happens in school,” he said.
While the ban was in line with the French constitution's separation of church and state, it did little to address issues of extremism and integration among the country's Muslim community, experts told The National.
“France has the largest and most alienated Muslim community in Europe. It is paying the price for decades of not focusing on the issue of integration,” said Ghanem Nuseibeh, of Cornerstone Global Associates, who has advised the French government on security and extremism.
Pupils return to school in France - in pictures
“While French security increased its presence in mosques, they still haven’t got to grips with aligning France as a secular state with a deeply religious Muslim community.
“The decision to ban abayas in schools was compatible with the ideas of the French Republic, but did not necessarily contribute to social cohesion.
“They need to realise that pretending to be a totally secular state does not work."
But an abaya ban was not enough for some leading figures on the right, who have called on the government to make children wear school uniform in state schools.
In the same radio interview, Mr Attal said he would announce a uniform trial in the autumn.
“I am not sure it's a miracle solution that will solve all school problems. But I think it merits testing,” he said.