Chirac said he also wanted to open the way for businesses to impose the same ban. Muslim groups have denounced the proposal as discriminatory, saying it will stigmatize France's Muslim population, the largest in Western Europe.
"Secularism is one of the great successes of the Republic," Chirac said in an address to the nation. "It is a crucial element of social peace and national cohesion. We cannot let it weaken."
Chirac said he would push for a law to be enacted in time for the school year that begins next autumn. Islamic head scarves, Jewish skullcaps and large crucifixes would fall under the ban.
Companies should also be free to ban the wearing of head scarves and other religious signs for reasons of safety or customer relations, Chirac said.
The proposed ban follows controversy in several schools as young Muslim girls defied school rules and wore headscarves to class, reports CBS News Correspondent Elaine Cobbe.
Adoption of a law seemed likely, as lawmakers from both sides of the political spectrum have voiced support for a law on secularism, insisting France must retain its separation of religion and state.
As expected, Chirac rejected a commission recommendation to establish the Jewish holiday of Yom Kippur and the Muslim Eid el-Kabir feast as school holidays.