Frederic Pechenard, director general of police and domestic intelligence services, told Europe 1 radio "I'm not here to frighten people," but there is serious evidence from reliable intelligence sources to suggest there is a risk of a major attack.
Pechenard said police had stepped up security and were being "extremely
He added that official national terror alert level had not been increased, although France's anti-terror posture is currently at alert level "reinforced red".
The next step, and top level "scarlet", would see the closing of airports and railway stations.
Pechenard said authorities were concerned about both the possibility of an assassination attempt on an important figure and a mass casualty attack on a crowded public area such as a metro train or department store.
Interior Minister Brice Hortefeux confirmed the terrorist threats on Monday and judicial officials said police are investigating intelligence that a female suicide bomber may be preparing a strike in Paris.
Known leaders of Islamist gangs have threatened France on Jihadi websites over the ban on the full-face Muslim veil after senators voted last week to pass a ban on the niqab.
The presence of French troops in West Africa is also a source of extreme tension.
In July they took part in a commando raid against an Al-Qaeda base in a bid to find French hostage and aid worker Michel Germaneau, who is thought to be dead.
Al-Qaeda's North African wing Al-Qaeda in the Islamic Maghreb claimed responsibility for killing Germaneau and vowed to avenge the raid.
The group has also claimed responsibility for the ongoing kidnapping in Niger of seven
foreign nationals working for French uranium mining firms, including five French citizens.
AQIM says it has taken the captives to Mali. France has sent an 80-strong military intelligence team equipped with spotter planes to the Sahara to track the gang.