France’s interior ministry said 416 were arrested in the early hours of Sunday, including 280 people in Paris.
Interior minister Laurent Nuñez said seven officers had been injured and called the unrest “absolutely unacceptable”.
Far-right leader Marine Le Pen wrote on X: “Only in France does a football club’s victory spark riots.”
“Only in France does everyone feel compelled to lock themselves in their homes on the evening of a victory to avoid being confronted with violence,” she said.
Players are due to take part in a victory parade on Sunday afternoon, which includes touring the Champs de Mars next to the Eiffel Tower and a reception held by French President Emmanuel Macron.
Last year, PSG’s European championship triumph was marred by clashes that left two people dead, including a 17-year-old boy.