"We have had more than 890 arrests. That's 45 percent more than last year," Interior Minister Laurent Nuñez told France Inter television.
The minister said nearly 180 police officers were injured.
The violent celebrations began on Saturday night, after Paris Saint-Germain defeated Arsenal in the Champions League final in Budapest on penalties.
Due to unrest following last year's title, 22,000 police were deployed to keep an eye on the celebrations. In Paris, several shopkeepers had barricaded windows and doors to prevent looting.
"Enough is enough. This is not football, not sport, not what we love," said President Emmanuel Macron in connection with Sunday's parade on the Champs Elysées.
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