Cazeneuve was speaking during a scheduled Euro 2016 Steering Committee meeting on security which took place in Paris as deadly explosions rocked Brussels airport and metro.
Cazeneuve said that the Brussels attacks "remind us tragically of the high level of threat we are confronted with".
But he said it would not affect security provided in stadiums and fan zones for the June 10 to July 10 tournament.
"We cannot permanently raise what is already a very high level since January 2015," said Cazeneuve, "but we can strengthen the measures".
"Our position is not to give in to terrorism," he continued. "This event can take place as the COP 21 took place (after the November attacks). However, we must have the flexibility, if necessary, to reconsider our position on some fan zones".
Sports Minister Patrick Kanner also attended the meeting during which measures were agreed for systematic pat-downs at fan zones, the use of metal detectors, demining services and video surveillance in zones welcoming 10,000 to 100,000 fans.
"It's an extraordinary exercise," said Kanner. "Never before has an event of this magnitude been monitored and secured at this level. The image of France is at stake, our ability to host events of this magnitude with
seriousness, composure and determination."
More than 2.5 million fans are expected to attend matches in ten host cities with a further 7 million expected in fan zones during the competition.
Fan zone security will cost up to 17 million euros ($19m), with UEFA promising 3 million euros before the November attacks, and are now examining a request for a further one million.
European governing body UEFA are responsible for security in the stadiums, team base camps, official hotels and the media centre, and will recruit 10,000 private security officers - seven percent more than planned before November 13.
Following Tuesday's attacks training for Belgium's friendly football match against Portugal was called off.
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"All our thoughts at this moment are with the victims (of the blasts). Football is not the priority today. Training cancelled," the Belgian Football Federation posted on its Twitter account.
There was no immediate word if the match, due to be played next Tuesday at the King Baudoin stadium in the Belgian capital, would go ahead.
Belgium are currently the top ranked team in the world and the game against Portugal is part of the team's preparations for the Euro 2016.
In another reaction to the blasts, the Travers la Flandre cycling race, which had been due to be held on Wednesday, was also called off.