OM have axed Evra, the former Manchester United captain, after he attacked a fan in Portugal last week.
"I hope that he can bounce back," said Giroud.
"I've written him a message to send my support. We had five great years together with the national team and he has always been a leader. It's difficult to speak of what he did, but it was instinct, something full of emotion. And I don't understand very well how supporters can come so close to the pitch like that.
"He's won numerous titles, he's a great player. I hope he can rebound, rediscover his happiness and finish in a different manner."