The French prime minister has said the country's security services are foiling terror plots and dismantling militant networks "every day".
Manuel Valls said about 15,000 people were being monitored for radicalisation as the country continues its drive against jihadist militants.
Previously the authorities said about 10,000 were identified as high-risk.
A boy of 15 was arrested at his home in Paris on Saturday on suspicion of planning an attack over the weekend.
Investigators said he had been under surveillance since April and he had been in touch with a French member of so-called Islamic State (IS), Rachid Kassim.
France has been under a state of emergency since IS attacks on Paris in November killed 130 people in what President Francois Hollande called an "act of war".
However, a recent commission of inquiry found the state of emergency was only having a "limited impact" on improving security.
It questioned the deployment of between 6,000 and 7,000 soldiers to protect schools, synagogues, department stores and other sensitive sites.
'There will be new attacks'
"Today the threat is at a maximum, and we are a target," Mr Valls told French media.
"Every day intelligence services, police, foil attacks, dismantle networks, track terrorists. There are about 15,000 people in France who are monitored, because these people are in the process of radicalisation."
In a sombre interview, the Socialist prime minister said: "There will be new attacks. There will be innocent victims."
Security is a central issue in the run-up to next year's presidential election but Mr Valls said proposals by the former French President, Nicolas Sarkozy, to set up special courts and detention centres were not the answer.
Mr Sarkozy, who announced in August he would run again for the presidency, gave an interview to the Sunday newspaper Le Journal du Dimanche (in French).
"Every Frenchman suspected of being linked to terrorism, because he regularly consults a jihadist website, or his behaviour shows signs of radicalisation or because is in close contact with radicalised people, must by preventively placed in a detention centre," he said.
Meanwhile, prosecutors charged one of the women arrested over a foiled attack near Notre Dame Cathedral in Paris.
Ornella G, 29, was charged with alleged involvement in a terrorist act and attempted murder.
Three other women were questioned by police, after a car packed with gas cylinders was found last Sunday close to the cathedral.
They are alleged to have been planning other "imminent and violent" attacks.
Paris prosecutor Francois Molins said on Friday that Ornella G's fingerprints had been found inside the car. She was known to intelligence agents as someone who was considering going to Syria.
She was arrested in southern France on Tuesday with her boyfriend, who has since been released.