However, a police spokesman said there were fewer problems than in 2005, when youths attacked trains in the Paris region and southeast of the country.
In an effort to maintain order, 25,000 police were on duty throughout the country during the night, including 4,500 in Paris, where the authorities banned fireworks and firecrackers.
Police said that by 0600 hrs (0930 IST) they had arrested 258 people nationwide, including two children aged eight and 10 who set fire to dustbins in the eastern city of Strasbourg.
Three children aged between 10 and 12 were arrested in a Paris suburb after they were caught carrying cans of petrol.
In the capital itself, almost 400,000 people welcomed in the New Year on the Champs Elysees and at the foot of the Eiffel Tower, where no serious incidents were reported.
Setting cars on fire has become a regular event in France during New Year's Eve celebrations, especially in the deprived suburbs that ring many cities.