Les Bleus have not won a match in a major tournament since beating Portugal in the 2006 World Cup semi-final.
And Nasri admitted: "Winning the Euro after the Premier League would be the ultimate dream.
"But we must beat England. If not, I will get it from every side when I return to City.
"There is no big ogre in our group like Spain or Germany. But the first objective is to reach the quarter-finals.
"We're under less pressure than in 2008 when France were the second best team in the world.
"This time we are outsiders and the first match against England, will set the tone."