The Manchester United full-back labelled 1998 World Cup winner Bixente Lizarazu and three other pundits "tramps" on French TV programme Telefoot.
The group had criticised the impromptu half-time talk he gave his team-mates during half-time of the 2014 World Cup qualifier with Belarus in September when he was only a substitute. France ended up winning the game 4-2.
Evra's comments came in the wake of the 3-0 win over Finland last week and the FFF have decided they require an explanation.
An FFF statement read: "Following the remarks made by Patrice Evra in an interview to Telefoot after France v Finland, president Noel Le Graet and coach Didier Deschamps, while recognising that no attack was made against the FFF, the France team, the coach or the players, have decided to ask
Patrice Evra to come to explain certain statements about the broadcasters."
The 32-year-old had accused the pundits of deliberately trying to tarnish his reputation.
He said: "There are some pundits with whom I will soon settle my differences with...they want to sell a lie to the French people that Evra is disliked. But that is not the case at all.
"I do not know what Lizarazu has against me. I was twice voted best left-back in the world, four times the best left-back in the Premier League. Him, I don't even know if he was ever voted best left-back in the world.
"I recall my first call-up to the national side, all the others shook my hand apart from him. Thierry Henry said to him, 'Oh Liza, here is the opposition'. And Lizarazu looked at me and said, 'Why? Someone told you that I was already retired?'.
"People have a good impression of me, it won't be these tramps who dirty my image. They must stop lying to the French people.
Lizarazu responded by saying: "His first cap I was no longer even there (in the squad) and yes I was once voted best left back in the world.
"He blames us for dirtying his image but he is doing a great job of it himself. As regards the timing, it sucks."