PARIS — At a moment when American lawmakers are reconsidering the broad surveillance powers assumed by the government after Sept. 11, the lower house of the French Parliament took a long stride in the opposite direction Tuesday, overwhelmingly approving a bill that could give the authorities their most intrusive domestic spying abilities ever, with almost no judicial oversight.

The bill, in the works since last year, now goes to the Senate, where it seems likely to pass, having been given new impetus in reaction to the terrorist attacks in and around Paris in January. Those attacks, which included the offices of the satirical newspaper Charlie Hebdo and a kosher grocery, left 17 people dead.

As the authorities struggle to keep up with the hundreds of French citizens who travel to and from battlefields in Iraq and Syria to wage jihad, often lured over the Internet, the new steps would give the intelligence services the right to gather potentially unlimited electronic data.

“The last intelligence law was done in 1991, when there were neither cellphones nor Internet,” Prime Minister Manuel Valls said.