Evra, charged by UEFA under article 15 of its disciplinary regulations, is now on the lookout for a new club and has been tipped to continue his career outside of Europe.
Speaking after France's 2-0 win over Wales on Friday night, Giroud told reporters: "I hope that he can bounce back. 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."
Giroud has played alongside Evra at international since 2011, although the last of the full-back's 81 caps came in November last year.