Manchester United full-back Evra captained Les Bleus at the 2010 World Cup, but was stripped of the honour and banned for his part in a player revolt against then-boss Raymond Domenech.
Laurent Blanc preferred Manchester City's Gael Clichy for much of his time in the French hot-seat, with Evra finding himself on the bench at Euro 2012.
He has been drafted back into the starting XI by Deschamps, a man he knows well from their time together at Monaco.
Evra is, however, yet to win over certain sections of the French fan base and will not be reinstated as on-field leader any time soon.
Deschamps told RMC: "I don't have any problems with Evra but he will not be captain under me and he knows why.
"I know him well because I had three years with him (at Monaco) but he is not looking for gifts from me, he will not be getting any favours.
"I am looking at things logically and he is picked on a sporting level. He is the best left-back in France."