Around 40 people were arrested in Paris after police used tear gas and water cannon against football fans hurling glass bottles at officers at the Eiffel Tower during the Euro 2016 final.

Crowds of supporters, some donning French or Portuguese flags, gathered at the base of the Paris landmark before and after Portugal's stunning 1-0 victory over France after they were refused entry to the fan zone which 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 order 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. Police in riot gear faced off with crowds, as at least one police truck fired water at demonstrators.

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, with piles of rubbish burning and firefighters were later deployed to put out larger blazes on the streets of Paris, including at least one car that was set on fire.

Meanwhile, nine people were taken into custody in the eastern city of Lyon for violent behaviour, insults or possession of fireworks and one officer was lightly injured by a spray can, police said.

Last week, riot police fired tear gas in clashes with youths on the Champs Elysees avenue in Paris after France's qualification for the Euro 2016 final.

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.

Portugal's shock win over France in the European Championship final was the country's first international title, though superstar Cristiano Ronaldo was forced to watch the match injured from the touchline.

The buildup to the football tournament had been overshadowed by fears of jihadist violence following November attacks that left 130 people dead. In the days before it kicked off, unions disrupted trains and grounded planes and uncollected rubbish built up in the streets in strikes and protests against labour reforms.

A man clashes with French riot police near the Champ-de-Mars fan zone in Paris before the start of the Euro 2016 final. Photo: AFP