Jewish leader Moise Cohen said such a ban would be seen as discriminatory and could “exacerbate emotions”.
Kamal Kabtane, head of the Grand Mosque of Lyon, told Reuters news agency that the proposal would resolve “nothing.”
The proposal follows an expert commission report on issues relating to religion and the state in France.
Christian groups have said the proposed ban could harm the integration of schools.
‘Respect of differences’
French President Jacques Chirac is to announce next week whether he supports the commission’s recommendation.
The ban would also include the Jewish skull-cap and large Christian crosses.
Former minister Bernard Stasi, who headed the commission consulted a wide cross-section of public opinion, including teachers, religious leaders, sociologists and politicians before handing in the report to the president on Thursday.
Although the report was into the wider question of French secularism, debate on the issue has focused on the wearing of Islamic headscarves in schools.
The commission’s recommendations would outlaw the Jewish kippa, large Christian crosses and the Islamic headscarf, which would be considered overt religious symbols.
“Discreet” medallions and pendants which merely confirm a person’s religious faith would be allowed.
“Muslims must understand that secularism is a chance for Islam,” Mr Stasi told a news conference on Thursday.
“Secularism is the separation of church and state, but it is also the respect of differences.”
The commission’s proposed law was intended so people of all religions could “live together in public places”, he said.
Mr Stasi stressed that the commission’s work did not target France’s Muslim community but was aimed at giving all religions a more equal footing.
The report also recommends that Yom Kippur – the Jewish Day of Atonement – and the Muslim Eid al-Kabir festival be celebrated in state schools.
French public life has a strong secular tradition which has existed since the revolution, but the commission has now recommended that the plan be enshrined in law.
Mr Chirac has hinted that he could back a formal ban.
He said he would study the proposals, consider the opinions of “political parties, the religious authorities and the representatives of public opinion” and discuss them with the prime minister before announcing his decision.
“The objective is to guarantee freedom to every French citizen, with the only restriction that the common rules be respected,” he said.
The issue has led to a number of celebrated cases where girls have been suspended or expelled for wearing headscarves to school.
Other schools have not acted.
France has the largest Muslim population in the European Union, with around five million people.