The proposal has attracted both fierce criticism and praise in the home of the largest Muslim community in the 27-member European Union.
Almost 10 per cent of France's 62 million population is Muslim.
Most French voters back a ban, polls have shown, but legal experts have warned that it could violate the constitution.
Many feminists from France's poor, multi-ethnic suburbs have spoken out in support of a ban, saying it could help young women who did not want to wear the veil but were forced to do so by their partners or families.
Others, however, see the ban as part of a rising hostility against Islam and its symbols, and argue that many Muslim women actually want to cover up.
The debate has spread as far as Afghanistan, where some women's rights activists expressed outrage at the French proposal, saying they disliked the burqa but women should be free to wear whatever they wanted.
The vast majority of Muslim women, in France and elsewhere, do not wear a full veil, but the niqab, which covers the face apart from the eyes, is widely worn on the Arabian peninsular and in the Gulf states.
The burqa, a shapeless full-body cloak that covers the face with a fabric grille, is worn in some areas of Pakistan and Afghanistan.
In France, the garments are widely identified with fundamentalist strains of Islam and with the isolation and repression of women in some communities, and politicians suspect their use is spreading.
"We're not going to let this phenomenon drift," Chatel said.
France's neighbour Belgium is also preparing legislation, and could become the first European country to ban the full veil when a bill goes before parliament during a plenary session that starts on Thursday.