Prime Minister Manuel Valls said the planned attack on one or more churches in the town of Villejuif just south of Paris was the fifth to be thwarted since a jihadist killing spree in the capital left 17 dead in January.
"The threat has never been as high. We have never had to face this kind of terrorism in our history," Valls told France Inter radio.
Sid Ahmed Ghlam, 24, was arrested yesterday after police stumbled upon his plans when he called paramedics saying he had accidentally shot himself in the leg.
Detailed plans to carry out an attack were also found.
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Police said his DNA was also linked to the murder of a young mother in Villejuif who was found shot dead in the passenger seat of her car on Sunday.
They are now trying to untangle the complex web of events and find who else may have been behind the attack, how did Ghlam shoot himself in the leg, and why did he kill young mother Aurelie Chatelain?
However a probe by intelligence services found nothing to go on, according to Interior Minister Bernard Cazeneuve.
The revelations about a planned attack that again escaped the radar of French intelligence services have highlighted the danger for France which is often singled out by jihadists as a prime target.
The arrest comes some three months after Islamic extremists gunned down 12 people at the Charlie Hebdo magazine, a policewoman and four others at a Jewish supermarket in a three-day reign of terror in the French capital.
Valls defended the overhaul of intelligence legislation saying it was long overdue and it "was not about tapping the phones of the whole population" and was about giving intelligence services "the means to be as effective as possible".