The bill includes a new offence - inciting to hide the face - with anyone convicted of forcing a woman to wear such a veil risking a year in prison and a $18,555 fine.
The interior ministry estimates that only 1,900 women cover their faces with veils in France out of an estimated five million Muslims, the largest such population in western Europe.
Some veil wearers in France say they have been increasingly harassed since debate over the planned law began nearly a year ago.
The bill is set to go before parliament in July and is widely expected to become law.
Sarkozy said last June that such veils are "not welcome" in France and that he wants a law banning them on the books as soon as possible.
However, the text, which could be amended in the process, foresees a six-month delay in its application to explain the law and mediate with those women affected, which means it wouldn't take effect until early in 2011.
Last month, Belgian politicians voted overwhelmingly to ban the wearing of full face veils in public.
The vote in the lower house of the federal parliament saw 136 deputies back a nationwide ban on clothes or veils that do not allow the wearer to be fully identified.
Taj Hargey, chairman of the Muslim Educational Centre in Oxford, UK, told Al Jazeera: "Muslims needs to adjust and adapt to Western society. There is no reason why women should cover their faces because it is not an Islamic requirement.
"If we enter a public domain, we need to follow the public rules and that means showing our faces."
France banned headscarves and other "ostentatious" religious symbols, from classrooms in 2004.
Some wearers of the veil in France say if the law is passed and they are arrested they will take their case to the European Court of Human Rights.
Draft law risks
The French government risks running up against the constitution following a warning in March from the Council of State, France's highest administrative body.
The council said such a ban was likely to violate the French constitution and the European Convention for the Protection of Human Rights and Fundamental Freedoms.
"There appears ... to be no legally unchallengeable justification for carrying out such a ban," it said.
Muslim leaders have said the face-covering veil is not required by Islam, but have also warned that a ban on the full veil risks stigmatising all Muslims.
Critics of the veil say such dress is an affront to gender equality and undermines the nation's secular foundations by bringing religion into the streets.