The 25-year-old was accused of insulting the referee as well as being involved in a row with his captain Hugo Lloris as Les Bleus were beaten by Spain in their quarter-final in Donetsk.
But the Paris St Germain player has sought to defuse the situation ahead of the FFF disciplinary meeting on Friday.
Menez told L’Equipe: “I sent a letter of apology (to the FFF). I apologised for my absence and for the accusations made against me. I am eager to turn the page.
“It’s annoying to have to face the committee – it is not good for the image. But I am making, and will make, efforts to improve myself every day.
“The story with Hugo, this was not really anything.
“It is something that exploded when there was nothing at all. In any case, I did not insult him. He himself said in L’Equipe that there was no problem between us.”
Of his clash with Italian referee Nicola Rizzoli, he added: “I was a bit upset. I did not start the game, we lost…
“(But) the action in question, I really did not commit any wrongdoing.
“It is true that it was not pretty. I want to apologise sincerely. Overall, in my case, it was an incident that should not have happened.”
Three other members of France’s squad – Samir Nasri, Hatem Ben Arfa and Yann M’Vila – are also the subject of disciplinary proceedings for various offences in Poland and Ukraine.