Dozens of youths shattered windows at a popular store on the Champs Elysees avenue on Sunday while hundreds of thousands of fans celebrated France's World Cup victory.
About 30 people, many wearing ski masks, broke into the Publicis Drugstore and later left with bottles of wine and champagne, some smiling and filming themselves with cellphones.
Some also threw objects including bottles and chairs at policemen who responded with tear gas.
"That's not how you celebrate," said a tearful bystander wearing a French team jersey.
As the hundreds of thousands of revellers gradually left the famous avenue, police used water cannon to disperse remaining troublemakers at around 11.30pm.
Elsewhere in France, authorities said clashes erupted in the southern city of Lyon between police and about 100 youths who had climbed on top of a police vehicle at an open-air showing of the match in the city centre.
Police fired tear gas to disperse the youths who responded by throwing objects and setting rubbish bins on fire, with the unrest causing some stampeding.
Ten people were arrested in Marseille, where two members of the security forces were injured in clashes, a police spokesman said.
In Frouard, a town outside the eastern city of Nancy, a three-year-old boy and two six-year-old girls were seriously injured after being struck by a motorcycle during the celebrations.
Authorities said the motorcyclist had fled the scene.
In the south-east city of Annecy, police said a 50-year-old man died after breaking his neck when he jumped into a shallow canal just when the final whistle blew to signal the end of the match.
And a man in his thirties died after crashing his car into a tree while celebrating shortly after the game in the small town of Saint-Felix in northern France.
Fans poured into the streets across the country after the country's second World Cup win, many waving flags and letting off smoke bombs.
About 4,000 police and security forces have been deployed across Paris during the World Cup festivities, and a vast security perimeter prohibiting vehicle access had been set up around the Champs Elysees.
The festivities will resume Monday when the victorious French squad will parade down the capital's most famous street at around 5pm, followed by a reception with President Emmanuel Macron at the Elysee Palace.
France remains on high alert following a string of terror attacks since 2015, which led to tough new anti-terror laws enacted last year that grant the police extended powers.
Meanwhile, Russian President Vladimir Putin has said the country was targeted by almost 25 million cyber-attacks during the World Cup, although he did not indicate who may have been behind them.
"During the period of the World Cup, almost 25 million cyber-attacks and other criminal acts on the information structures in Russia, linked in one way or another to the World Cup, were neutralised," Mr Putin said during a meeting with security services ahead of the final.
The president, whose comments were reported by the Kremlin on Monday, gave no information on the nature or possible origins of the cyber-attacks.
"Behind this [World Cup] success lies huge preparatory, operational, analytical and information work, we operated at maximum capacity and concentration," Mr Putin said.
Russia itself has been repeatedly accused by western countries of conducting cyber-attacks.
On Friday, 12 Russian military intelligence officers were charged with hacking Hillary Clinton's 2016 presidential campaign and the Democratic Party in a stunning indictment three days before President Donald Trump's meeting with Mr Putin in Helsinki.
The charges were drawn up by Special Counsel Robert Mueller, the former FBI director who is looking into Russian interference in the November 2016 presidential elections and whether any members of Trump's campaign team colluded with Moscow.