French police have foiled five terror attacks in recent months, Prime Minister Manuel Valls has said.
He said the latest was a planned attack on churches in Villejuif outside Paris.
An Algerian man was arrested on Sunday over the alleged plan, after he apparently shot himself by accident and called an ambulance.
France stepped up security following attacks on Charlie Hebdo magazine and a Jewish supermarket in January which left 17 people dead.
"The threat has never been so high," Mr Valls told France Inter radio. "We have never had to face this kind of terrorism in our history."
He said 1,573 French citizens or residents had been implicated in "terror networks" - 442 of those were currently believed to be in Syria.
Ninety-seven of those had died in Syria or Iraq, including seven while carrying out suicide attacks, he added.
His comments come a day after the French authorities revealed they had arrested a 24-year-old Algerian man on suspicion of planning to attack "one or two churches" in Villejuif.
Sid Ahmed Ghlam, a computer science student, was detained on Sunday after calling an ambulance having apparently accidentally shot himself in the leg.
When police arrived at the scene they found an arsenal of live weapons in his car and home, and documents detailing plans to attack a church, prosecutors added.
Mr Valls said investigators are now searching for possible accomplices in the planned attack.
"This type of individual does not act alone," he told France Inter.
Mr Ghlam has also been linked to the murder of a 32-year-old woman, Aurelie Chatelain, who was found dead in her car in Villejuif on Sunday.
Prosecutors said traces of her blood were found on one of Mr Ghlam's jackets.
French Interior Minister Bernard Cazeneuve said Ghlam was known to security services as having expressed a wish to travel to Syria to fight with Islamist militants.