Organising committee chairman Jacques Lambert warned against considering cancelling or moving Euro 2016 in the wake of the Paris attacks.
Officials say 129 people were killed and 99 critically injured in what appeared to be coordinated strikes across the French capital on Friday, including a blast at the Stade de France.
The deaths have raised fears ahead of Euro 2016, scheduled to be hosted by France in June and July next year.
But Lambert said it was wrong to be thinking about alternative plans for the tournament.
"The risk had gone one level up in January [with the attack on Charlie Hebdo], it has just gone higher," he told radio station RTL.
"We will make the decisions we need to make so that the Euro finals can be held in the best security conditions.
"Security in stadiums works well, the risk is more in the streets, in spontaneous gatherings."
Lambert added: "Wondering whether Euro 2016 must be cancelled is playing the game of the terrorists."
The French Football Federation (FFF) and tournament organisers are reportedly set to meet on Monday to discuss safety.