Jacques Chirac said on Wednesday that a law is necesary to safeguard the nation's secular identity.
He said: "The Islamic veil... the kippa and a cross that is of manifestly excessive dimensions - these have no place in the precincts of state schools. State schools will remain secular. For that a law is necessary."
The president was giving his verdict on the findings of a committee of experts which recommended last week a ban on "conspicuous" insignia in schools.
He said the law should be in effect by the start of the next school year in September 2004.
"Secularism is one of the great conquests of the Republic. It is an element crucial to our social peace and national cohesion. We cannot let it weaken. We must work to reinforce it," he said.
"The Islamic veil... the kippa and a cross that is of manifestly excessive dimensions - these have no place in the precincts of state schools. State schools will remain secular. For that a law is necessary"
Chirac also rejected a second committee recommendation that the Muslim Eid al-Kabir and the Jewish Yom Kippur festivals be introduced as annual holidays in state schools.
"However, I do not think any pupil should have to say sorry for being absent on a major religious holiday... as long as the establishment has been informed in advance," he said.
The headscarf issue has become the focus of a growing debate over how best to integrate France's five million-strong Muslim minority.
Ardent secularists fear the headscarf is an outward sign of a refusal to assimilate fully into French society.
However, Chirac said a firm stance against headscarves must be accompanied by an greater determination to involve Muslims in society.
"I share the feeling of incomprehension, of disarray and sometimes even of revolt by those young French people - immigrants by origin - whose job applications go in the bin because of the sound of their name," he said.
"All the children of France, whatever their background, whatever their origin, whatever their belief, are daughters and sons of the republic. They must be recognised as such, in law but above all in the facts (of everyday life)."
However, many Muslims in France argue the hijab is a religious obligation which is perfectly compatible with France's secular principles.
And a growing number of voices have warned of the dangers of a law that targets an already resentful Muslim minority.
Leaders of the three main religions have all expressed doubts, with the French Council for the Muslim Religion saying that "the spirit and general tone of the report stigmatise one section of the nation, and take no account of the reality of Islam in France".
The Christian churches have said "any law seen as discriminatory by some French citizens could have in the short term consequences that are more harmful than the benefits".
There are more than five million
Muslims in France
And Chief Rabbi Joseph Sitruk said "it is not by prohibiting this or that insignia that you make people more tolerant".
Moreover, a feminists' group - Feminists for Equality - has launched a petition against a law, arguing that "the girls and women who wear the headscarf are not the fifth column of some foreign power - they are an integral part of our society".
It is estimated that several thousand girls wear the headscarf in French schools, but the controversy has been driven by a handful of high-profile cases in which pupils were expelled from school for refusing to uncover themselves.