Cazeneuve praised the work of over 100,000 police, gendarmes, private security agents and soldiers who secured the event, adding that 1,550 people had been arrested during the tournament.
"Despite the very high threat, Euro 2016 was a success," said Cazeneuve.
France had been on high alert throughout the tournament, after two major terror attacks in 2015 which left 147 people dead.
Cazeneuve said that overall in 2016, 150 people had been arrested in France for "terrorist activities".
However aside from hooligan violence at the start of the European championship and clashes between fans and police on the night of the semi-final and final in Paris, the tournament went off without a hitch.
"Today we can say that it is France who won. Maybe not in the area of sports, but our country won in its capacity to organise" the event, said Sports Minister Patrick Kanner.
"We were all haunted by fear of a terrorist attack. We were lucky that nothing serious happened and it is a great relief," said Jacques Lambert, the head of the tournament's organising committee.
Cazeneuve said that of those arrested during the month-long event, 59 people were convicted to jail time or suspended sentences, 64 people were expelled from the country and 32 were refused entry.
However despite the success of the tournament he warned that "the terrorist threat remains" in France.