"We've had more than 890 arrests. In total, that's 45 per cent more than last year," Interior Minister Laurent Nunez told broadcaster France Inter, adding that nearly 180 law enforcement officers had been injured.
Celebrations were blighted by clashes between youths and police in Paris and other cities, cars set on fire and shops looted.
On Sunday evening, President Emmanuel Macron received the team at the Elysee Palace. While he said PSG were an "immense pride" for France, he denounced the "unspeakable" violence.
"Enough. We are fed up," he said.
"This is not football, this is not sport, this is not what we love," he added.
One man died riding his motorbike around the Paris ring road in celebration, while authorities reported stabbings and other attacks.