Blanc: M'Vila improving after ankle injury
"M'Vila is getting better, much better," Blanc told a news conference, adding that fellow midfielder Blaise Matuidi, who has a thigh problem, was also improving.
"There could be a nice surprise."
M'Vila, regarded as Blanc's first-choice holding midfielder, suffered the injury in France's 2-0 win against Serbia in a warm-up game last Thursday.
France take on Estonia in Le Mans in their final warm-up on Tuesday before flying to Ukraine the following day.
They face England in Donetsk, then take on co-hosts Ukraine in the same city on June 15 and Sweden in Kiev on June 19.