Thousands of people poured into the streets of Paris for the match and to revel in PSG's triumph in the final held in the Hungarian capital Budapest late Saturday.
But some mobs clashed with police, around 22,000 of whom were deployed across France after unrest last year when PSG also won the competition.
Highlighting an increased use of fireworks directed at law enforcement, Interior Minister Laurent Nunez said in a press briefing 57 security forces were injured and that there had been "219 participants injured in France, including eight seriously".
The Paris public prosecutor's office announced the death of a young man in his twenties after he crashed head-on into concrete blocks on a Paris ring road exit ramp on his motocross bike.
Another young man was seriously injured in a knife attack in Paris allegedly over a robbery, the prosecutor's office added.
Nunez said a small number of thefts and lootings had taken place in around fifteen cities across the country and incidents of violence were recorded in 71 municipalities.
The 780 arrests was a 32 percent increase compared to the celebrations of PSG's Champions League win last year, the minister noted.
Victory parade
Around 100,000 people are expected to gather for a parade including the players on Sunday afternoon on the Champs-de-Mars in front of the Eiffel Tower, before being received at the Elysee Palace by President Emmanuel Macron.
Nunez promised "a strong law enforcement response" during the players' return celebrations and fines for "obstructing traffic" in the event of any intrusion onto the Paris ring road.
The district mayor of Paris's 8th arrondissement -- home to the famed Champs-Elysees where 20,000 people converged after PSG's victory -- called for "zero gatherings" on the iconic avenue as the only way to avoid further violence.
On Saturday night, the "Champs-Elysees avenue and its surroundings ceased to be a place of celebration and became an arena of urban guerrilla warfare", the town hall said in a statement.
"Since it has become impossible to celebrate a match without descending into riots, the only common sense response is a new doctrine: 'zero gatherings'," it demanded.
Nunez dismissed the idea saying it would "tie up almost half of the security deployment". Nearly 6,000 police and gendarmes have been deployed for security during the celebrations on Sunday.
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