The law has already been passed by the National Assembly but still has to be vetted by the Constitutional Council, France's highest constitutional authority. It would make France the first European country to outlaw the burqa or niqab.
Offenders would be fined 150 euros ($189) or be required to take part in a citizenship class.
"The full face veil dissolves the identity of a person in that of a community," Justice Minister Michele Alliot-Marie said before the 246-1 vote. "It challenges the French model of integration based on the acceptance of the values of our society." Most opposition senators abstained in protest.
Alliot-Marie said the ban had nothing to do with religion. It reaffirmed the French values of equality and dignity of all individuals and would prevent women from simply becoming faceless members of a larger ethnic community.
France's five-million-strong Muslim minority is Western Europe's largest, but fewer than 2,000 women are believed actually to wear a full face veil. Many Muslim leaders have said they support neither the veil nor the law banning it.
The bill, which critics say stigmatises Muslims, bans people "from wearing, in a public place, garments designed to cover the face". It is due to take effect after a six-month period aimed at informing veiled women about the law.
Bans gain support In Europe
Forcing someone to cover the face would be punishable by a one-year prison sentence and a 30,000 euro fine. The law does not apply for carnivals or artistic events.
The ban's backers say burqas, which cover the body from head to toe, and niqabs, which leave only the eyes uncovered, demean women and are a threat to public security.
The Council of State, France's top legal advisory body, has questioned whether a ban is compatible with the constitution and the European Convention on Human Rights. The Council of Europe has also said veil bans deny women a basic right.
France had already banned the wearing of Muslim headscarves in schools and the civil service, although female university students may wear them.
Movements to ban the garments have gained ground across Europe. Polls in Italy, Spain, Germany and Britain have indicated widespread support.
The Belgian lower house of parliament voted in April to ban all clothing that covers or partially covers the face, but it was dissolved before a final vote could be taken (see 'Background').
Spain, where some towns, including Barcelona, prohibit full face veils in public buildings, is considering a national ban, while a coalition ally of Prime Minister Silvio Berlusconi is pushing for legislation to outlaw them in Italy.
The French National Assembly voted 335-1 for the ban, with opposition Socialist and Green lawmakers also abstaining.
The same day, French police evacuated tourists from the landmark Paris Eiffel Tower and a metro station following bomb alert, but searches found no explosives, police said.
A police spokesman said the company that operates the Eiffel Tower received an anonymous call around 20:30 local time, saying a bomb had been planted there.
"Special units were on site and have inspected the entire structure and nothing was found. About 2,000 people were evacuated from the perimeter," the spokesman said.
Another anonymous call led to a bomb scare at the Saint-Michel metro station, which was evacuated briefly, the police spokesman said.
The station was the site of a July 1995 bomb claimed by Algeria's Armed Islamic Group (GIA), which killed eight and wounded 80.
French police have been on high alert due to the anniversary of the September 11, 2001 attacks in the United States. The press also reports that the police took the alerts seriously because of the burqa ban.
(EurActiv with Reuters.)