The French capital was subject to an attack for the second time this year in a series of incidents across the city, which resulted in the deaths of at least 129 people.
French Football Federation president Noel Le Graet revealed that he was worried about safety issues for the competition, but Lambert believes that cancelling the tournament would only play into the hands of the terrorists.
"The risk had gone one level up in January, it has just gone higher," Lambert 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.
"Wondering whether Euro 2016 must be cancelled is playing the game of the terrorists."
The Stade de France was the subject of a failed attempt by suicide bombers as an attacker was stopped at the entrance to the ground before he detonated his device.