The French senators backed a first reading of the bill by 229 votes to 106.
The right-wing Republicans voted in favour, as did President Emmanuel Macron's Republic on the Move and a centre-left grouping, the RDSE.
The Socialists, Communists and two former ecologists voted against.
The draft will now go back to the lower house, the National Assembly, for debate in October.
Replacing state of emergency
The proposed law, a Macron campaign pledge, will replace a state of emergency imposed after the November 2015 Paris attacks, which left 130 people dead.
The state of emergency gives the authorities extensive powers to place people under house arrest, order searches of premises and ban public gatherings without the prior approval of a judge.
Despite complaints that many of its measures were used to block protests rather than against terrorism, the state of emergency was extended for a sixth time earlier this month.
Some of the state of emergency's provisions will become permanent under the proposed law, a move rights groups say is draconian.
The bill aims to tighten control over air and sea travellers and change the law on monitoring of wireless communications.
The Senate did amend it to put a time limit of 31 December 2012 on the extended right to stage searches of premises and surveillance of individuals and controls on their movements.
They also imposed an annual review of the law's efficacy.
Interior Minister Gérard Collomb defended the bill, saying it was necessary to combat the "ever-present" terror threat.
"We want to get out of the state of emergency, but we can't do so without counter-terrorism controls in place," he said.