French Interior Minister Laurent Nuñez said around 110,000 people demonstrated in Paris, while the nationwide turnout reached 550,000.
He said most of those detained were adults with no links to the student movement. At least 60 law enforcement personnel were injured, including two who were taken to hospital unconscious.
Nuñez blamed far-left extremists for the violence, saying there was a clear intention to target public buildings. Incidents of looting and attempted looting were reported in several cities, including Paris, Rouen, Nantes, Toulouse and Marseille.
The French president said violence would not be tolerated in the country and warned that those responsible for damaging or attacking regional administrative offices, businesses and municipal buildings, or looting municipal offices, would face punishment.