"Since the start of the competition, (police) have carried out more than 1,000 arrests, leading to 600 custody orders and 56 convictions," Interior Minister Bernard Cazeneuve told La Provence newspaper.
Supporter clashes around the England-Russia match in Marseille marked the start of the month-long tournament which runs until July 10th.
Cazeneuve said 34 people have been ordered expelled from France.
He did not give a breakdown, but said many were linked to the violence before the June 11th game in Marseille at which 35 people were injured. At least 23 Russians have been expelled.
French authorities have mobilised about 90,000 security forces and private guards for Euro 2016.