The move came as part of the State Department's continuous efforts to alert Americans travelling abroad with information about safety.
And on Tuesday, France was among the countries singled out as potential terror targets.
"Euro Cup stadiums, fan zones, and unaffiliated entertainment venues broadcasting the tournaments in France and across Europe represent potential targets for terrorists," the State Department warned.
The travel warning is in place until the 31st of August, with authorities also noting that the Tour de France will be taking place for most of July - without giving a specific warning about the race.
The State Department added that citizens should be vigilant in public places and when using mass transportation, to avoid crowded places and to monitor media.
It also suggested Americans should be prepared for additional security and should stay in touch with family and "ensure they know how to reach you in the event of an emergency".
France is taking security at Euro 2016 extremely seriously, announcing last week that it will deploy more than 90,000 police and security guards for the tournament, which runs from June 10th to July 10th and will be held at stadiums across the country.
Deputy mayor of Paris Jean-François Martins told The Local recently that the city was "prepared and determined" when it came to safety around the event.
He pointed out the fact the Stade de France bombers could not get inside the stadium on November 13th proves that authorities security checks and systems work.
"We have been preparing for this for many years and that includes how to deal with the terror threat," he said, before refusing to go into detail about the security operation, stressing it needs to remain confidential.