French police arrested around 40 people for violence and other offences before and after France's defeat to Portugal in the Euro 2016 final in Paris on Sunday, police said.

Police used tear gas and rounded up supporters who pelted them with bottles at the foot of the Eiffel Tower after they were refused entry to the fan zone, which was closed after it was packed to its 90,000 capacity, Paris police said.

Other arrests took place outside the Stade de France where the match was played. They were for public disorder offences.

The base of the Eiffel Tower was engulfed in clouds of tear gas as riot police repelled the youths, who started fires on the pavement and threw bottles and other objects at the police lines, AFP photographers said.

The police, who had posted a message on Twitter and issued warnings in the Metro informing supporters the fan zone was full, used water cannon to extinguish the blazes.

The ground was littered with broken fencing and shattered glass as evening fell, and firefighters were later deployed to put out larger blazes on the streets of Paris near where the clashes took place.

Some of the demonstrators wore French flags knotted around their necks in a sign of support for the home side, but fans donning Portuguese regalia were also seen taking part.

Earlier clashes between fans at the June 11 England-Russia match in Marseille left 35 people injured in violence that French prosecutors have largely blamed on around 150 "well-prepared" Russian supporters who carried out targeted attacks on England supporters.