France, eliminated in the group stages of both Euro 2008 and the 2010 World Cup, face England on June 11 in Donetsk before playing co-hosts Ukraine and Sweden.
"The last eight is certainly within our reach. We have the potential to qualify," Nasri told reporters at France's Clairefontaine training facility.
"Obviously, it's better to play England first, when Rooney is still suspended," he added.
The Manchester United striker is suspended for two games following his sending off for kicking Miodrag Dzudovic during the final qualifier against Montenegro in October.
The French players will mostly focus on resting their bodies and minds after an exhausting season, one which ended in particularly dramatic fashion for Nasri, when City snatched the Premier League title in the final seconds.
"I only realised how crazy it had all been when I watched the game again," Nasri said, referring to the two stoppage-time goals which helped City defeat Queens Park Rangers to win the club's first league title in 44 years.
"I am a bit tired, I did not sleep enough. We did a lot of partying. But I will recover fast here," he added.
"It was a fantastic moment for the club and for me as well.
"I managed to make an impact at the end of the season. I also think I improved mentally and defensively at City."
