National Police Chief Michel Gaudin said police were taking every precaution, including banning public gatherings, a day after the calls for violence on Saturday evening in Paris were posted on internet blogs and sent in text messages to mobile phones.
"This is not a rumour," Gaudin told a news conference, citing Paris' best-known landmarks among potential targets.
"One can easily imagine the places where we must be highly vigilant."
However, no trouble in Paris had been reported overnight on Saturday to Sunday.
Unrest has receded since the government declared a state of emergency on Tuesday, empowering local authorities to invoke exceptional security measures such as curfews.
Despite heightened security around the country, violence broke out on Saturday night in the southeastern city of Lyon. Police fired tear gas to disperse stone-throwing youths at the city's historic Place Bellecour. It was the first time in 17 nights of unrest across France that youths and police clashed in a major French city.
In separate incidents on Saturday night in the southern city of Carpentras, rioters rammed burning cars into the side of a retirement home and a school, national police spokesman Laurent Carron said.
Violence in Lyon on Saturday
caused police to fire tear gas
A primary school and linen store were set ablaze in Carpentras, he said.
Police counted 315 cars torched and said 161 people were arrested across France overnight as of 4am (0300 GMT).
A police officer was injured after he was hit with a metal ball dropped from an apartment building in the northern Paris suburb of La Courneuve, Carron said.
Arsonists set an electronics store on fire on Saturday night in Blangnac, on the outskirts of Toulouse, the regional government said.
Hours earlier, regional authorities had imposed a weekend curfew on Lyon, France's third-largest city, which barred youths under 18 from being outside without adult supervision between 10pm and 6am.
Forty towns, suburbs and smaller cities have imposed curfews on minors to clamp down on violence that started on 27 October in a tough Paris suburb and has grown into nationwide unrest marked by extensive arson and clashes with police.
Youths under 18 were put under
a weekend curfew in Lyon
Paris police took the exceptional step of banning all public gatherings that could "provoke or encourage disorder".
Police spokesman Hugo Mahboubi said it had been at least a decade since the authorities had imposed any similar ban on gatherings in the French capital.
As unrest continued, calls for peace and political change were mounting.
Police allowed an evening demonstration in Paris's Latin Quarter, which drew several hundred people protesting against the state-of-emergency measures.
Many of the protesters were left-wing political groups and members of Communist-backed unions.
They called for the resignation of Interior Minister Nicolas Sarkozy, who has been accused of inflaming the violence by calling troublemakers "scum".
Protesters have called for the
resignation of Nicolas Sarkozy
Under tight police surveillance, protesters called the strict new measures a provocation that would not resolve violence or answer the long-term problems that caused the unrest. A similar rally in the southern city of Toulouse drew about 700 people.
The violence started in the northeastern Parisian suburb Clichy-sous-Bois on 27 October.
About 100 youths rioted to protest against the accidental deaths of two Muslim teenagers, who were electrocuted while hiding from police in an electricity substation. It quickly triggered rioting in low-income housing projects across the country that have been centres for unemployment and alienation.
The unrest has forced France to confront its failure to integrate minorities and the anger simmering among its large African and Arab communities.