Senators backed a first reading of the bill by 229 votes to 106, meaning the text will now be handed to the lower house, the National Assembly, for debate in October.
The new laws -- a campaign pledge of President Emmanuel Macron -- will replace a state of emergency imposed after the November 2015 terror attacks in Paris that left 130 people dead.
Under the state of emergency, authorities have the power to place people under house arrest, order house searches and ban public gatherings without the prior approval of a judge.
Some of them will become permanent under the proposed law, a move rights groups including Amnesty International and Human Rights Watch say is draconian.