Islamic State claimed responsibility after 129 people were killed and 352 wounded on Friday, saying it sent militants strapped with suicide bombing belts and carrying machine guns to various locations in the heart of the French capital.
"The risk had gone one level up in January, it has just gone higher," Euro 2016 chief Jacques Lambert told French radio 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.
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"Wondering whether Euro 2016 must be cancelled is playing the game of the terrorists," said Lambert.
There was one bombing near the Stade de France on Friday, killing three, as the national team were playing a friendly against Germany inside the venue.
Euro 2016 will be held from June 10-July 10.
(Reporting by Julien Pretot; Editing by Tony Jimenez)
