But there was otherwise positive news on Les Bleus' defensive midfield injury crisis, with Blaise Matuidi and Alou Diarra both making good progress in their recovery from setbacks.
M'Vila has been a doubt for the game since turning his ankle in a pre-tournament friendly against Serbia on May 31 and team doctor Fabrice Bryand considers it likely the Rennes star will miss out against England.
"His progress is good but we do not want to aggravate the injury," Bryand told L'Equipe. "We are not optimistic for the 11th.
"We will increase his workload and see if his ankle swells again or if he suffers any ill effects. We will pay close attention to the player's recovery."
The 21-year-old has been linked with a move to Arsenal after establishing himself as a key player in Ligue 1, and his likely absence will be a boost to Roy Hodgson and his squad.
But France should have a strong replacement available, with Matuidi and Diarra on the mend after their respective hamstring and knee complaints.
Bryand admitted Marseille midfielder Diarra "gave us a big scare" when he felt pain in his knee, having been pencilled in as the man to fill the problem position.
But he added: "He suffered a slight inflammation of the tendon behind the right knee, but it is going well.
"Yesterday [Thursday], we did not take any risks because we were training on a synthetic pitch, but he was initially going to train."
On Paris St Germain's Matuidi, he added: "His progress is very satisfactory. He has started a special program and we will accelerate that and bring him back gradually.
"Everything depends on how he reacts."