"Orders to be vigilant have been strengthened," ahead of the Turkey-Croatia game Paris police spokeswoman Johanna Primevert told the AFP news agency on Sunday.
Following the violence in Nice and Marseille, right-wing MP and regional council president Eric Ciotti called for a ban on the sale of alcohol to take away in areas where football supporters gather, a measure that has already been taken in the eastern city of Lens, which hosts the England-Wales match on 16 June.
British police help French
British police have sent teams to help their French colleagues handle fans from the UK's three participating teams - England, Wales and Northern Ireland.
They are believed to number between 300,000 and 500,000, although only 250,000 have tickets, leading to special concern over those who do not.
But many of those involved in the fighting were not known to British or Russian police and so had not been banned from entering France, according to French Interior Ministry spokesman Pierre-Henry Brandet.
Some 2,000 known hooligans were banned from leaving the UK during the tournament and had to hand their passports over to police on 1 June.
Calls for alcohol ban
One person was arrested in Nice shortly before midnight Saturday, according to mayor Christian Estrosi, following fighting between local youths and Northern Irish fans that left seven people injured.
The clashes came ahead of a Poland-Northern Ireland match due to start at 6.00pm on Sunday.
Ten people - a Briton, an Austrian, a German and some French and Russian nationals - were in detention on Sunday after their arrest on Saturday in Marseille with several due to appear in court on Monday morning.
Two British nationals who had been arrested during violence on Friday were jailed after appearing in court on Saturday, while a British minor and a French woman were freed on parole and banned from attending matches, with the boy's ticket to the England-Russia match cancelled.
A French man arrested Friday was still waiting to appear in court.
French police defend handling of Marseille clashes
"I don't want to hear it said any more that the operation was not up to the challenge," Marseille police prefect Laurent Nunez said on Sunday, claiming that "the police prevented some very serious violence" by dispersing "belligerents".
"There was not failure, in so far as the rapid and effective intervention of the forces of order allowed us to contain the incidents," commented Marseille police commissioner Antoine Boutonnet, while Interior Minister Bernard Cazeneuve insisted in a statement that the risk of hooliganism had been fully accounted for "in the same way as other threats, notably terrorism".