The travel alert late on Tuesday, which expires on 31 August, made no mention of specific threats to Euro 2016 matches or other events, but warned US citizens to "exercise vigilance" and "avoid crowded places".
"The large number of tourists visiting Europe in the summer months will present greater targets for terrorists planning attacks in public locations, especially at large events," the alert said.
"Euro Cup stadiums, fan zones, and unaffiliated entertainment venues broadcasting the tournaments in France and across Europe represent potential targets for terrorists, as do other large-scale sporting events and public gathering places throughout Europe."
France's national stadium, the Stade de France, was one site targeted during the 13 November Paris attacks that left 130 people dead.
Suicide bombers detonated explosive belts near gates at the stadium as France played Germany in a friendly match.
France has already extended its state of emergency - imposed after the attacks - through 26 July.
Euro 2016 football tournament is expected to draw up to 2.5 million people, according to the State Department, Sky News reported.
The agency said US authorities are working "closely with our allies and will continue to share information with our European partners that will help identify and counter terrorist threats".