France failed to reach the knock-out stages at the 2008 European Championship and the 2010 World Cup.
Paris: A third consecutive early exit at a major tournament would be a "complete disaster" for France, midfielder Yann Mvila said on Friday.
Two years after losing the 2006 World Cup final to Italy on penalties, France failed to reach the knock-out stages at the 2008 European Championship.
They suffered the same blow at the 2010 World Cup, where the players shocked the world by boycotting training to support Nicolas Anelka after the forward was kicked out of the squad for insulting then-coach Raymond Domenech.
With France trying to restore their reputation, they cannot afford another exit, Mvila told a news conference at the Clairefontaine training camp.
"It would not only be a failure, it would be a complete disaster," the Stade Rennes midfielder said.
France's players have learned to be cautious about the country's prospects at major tournaments but Mvila, who is heading for his first major finals with Les Bleus, was more optimistic and said their only aim was winning the title.
"We go to the Euros to make it [a] victory," he said, adding that France should be much higher than 16th in the FIFA world rankings. "We're more a top-five team," he said.
France are in Group D and play England on June 11 before facing co-hosts Ukraine four days later and Sweden on June 19.