Earlier, the interior minister said the security forces would be “firm” in their response to violence.
“We are a great country for maintaining public order. We allow freedom of assembly, but not excesses,” he said.
There was similar violence when PSG won the same trophy last year, with celebrations turning deadly.
Thousands of officers had been deployed this time to curb unrest that disrupted bus, train and rail services in Paris.
The vast Champs-Élysées was swarmed by fans shortly after the local team won in a penalty shootout.
Footage shows flares being set off, electric bikes burning on roads and revellers smashing the glass of at least one shopfront. Police fired tear gas to disperse crowds in the city centre.
Paris police made 480 arrests, with 277 taken into custody, including 82 minors.
The figures were provisional, the Paris prosecutor’s office said. It added that offences ranged from attacks on officers to attacks on property, theft, as well as illegal possession of weapons.
The circumstances surrounding the death of the 24-year-old near Porte Maillot in the Paris ring road remain unclear. Some witnesses said he was riding a motorcycle when he crashed into concrete blocks.
A teenager was also in critical condition following a brawl in another area of Paris. It is not clear if they were involved in the football-related rioting.
