Dissenters have 10 days to challenge the measure in the constitutional Council watchdog, but that is considered unlikely.
Legislative leaders said they wanted the constitutional Council to examine it.
"This law was the object of long and complex debates," the Senate president, Gerard Larcher, and National Assembly head Bernard Accoyer said in a joint statement explaining their move. They said they want to be certain there is "no uncertainty" about it conforming to the constitution.
The measure affects fewer than 2,000 women, but Muslims believe it is one more blow to France's second religion, and risks raising the level of Islamophobia in a country where mosques, like synagogues, are sporadic targets of hate. Some women have vowed to wear a full-face veil despite the law.
The proposed law was passed overwhelmingly by the National Assembly on July 13. The green light from the Senate would make it definitive once the president signs off on it barring amendments and an eventual legal challenge.
In France, the terms "burka" and "niqab" often are used interchangeably. The latter is a full-face veil, often in black. Unlike the burka, it does not obscure a woman's eyes.
CBC News - World - French Senate bans burka