"When I think about the European Championships, I have concerns, as many people do in Europe. Concerns that this peaceful event could be disturbed," Gauck said, according to national news agency DPA.
Hours before the tournament was due to kick off Friday, Gauck noted that France has had the "bitter experiences" of suffering devastating jihadist attacks, and had boosted security for the meeting of Europe's best national teams.
But, Gauck noted, "there are people who want to hurt others".
"And I hope that our French neighbours will be able to see their beautifully-planned event through to a beautiful end," said Gauck.
Euro 2016 kicks off later Friday when France face Romania at the Stade de France in Paris, outside which three jihadists blew themselves up at the start of the November 13 attacks on the French capital.