Politicians say they are determined not to see schoolgirls covering their hair in the classroom regardless of their beliefs.
Religious symbols such as Islamic veils have no place in French state schools, Prime Minister Jean-Pierre Raffarin has said.
Schools "should not be the place where people display their religious affiliations", Raffarin said in an interview on the M6 channel on Sunday.
While proclaiming himself in favour of everyone being free to practise their religion, he said he remained opposed to "ostentatious expression of religious conviction".
However, France's largest Muslim organisation has said any new legislation to ban veils would be "unjust".
Lhaj Thami Breze, president of the Union of French Islamic Organisations, said: "There is a French government commission ongoing into this question and I think people should wait for the result of that. But we do believe it would be unfair to ban the headscarf."
He added: "The interior minister, Nicolas Sarkosy, has given us guarantees this will not happen. But maybe there will be some sort of compromise - we may agree to some sort of hat which covers the head."
And Mr Breze said there was no contradiction between France's ardent secularism and Islam.
There are five million Muslims in
"We respect secularism and sincerely believe it respects Islam and all religions. Our argument is only with secular extremists who want to ban the veil. People often talk of religious extremists but there are secular extremists as well."
The question of traditional Islamic dress is at the centre of deliberations by a national commission on France's secular principles.
While France is mainly Catholic, five million of its 58 million inhabitants are Muslim.
The debate over whether Muslim women have the right to wear headscarves at school, at work or even on identity photos, regularly causes a furore in France which is fiercely proud of its secular nature.
Although the headscarf is officially banned in French schools some feel the current law is too vague and is being abused.
Some Muslim groups say the ban is an attack on Islamic culture which alienates Muslims from French society rather than endears them to it.