In the World Cup qualifying match against Belarus, substitute Patrice Evra gave the team an impromptu half-time talk.
This led to criticism from Lizarazu and three other pundits.
Evra responded by calling the group "tramps" and "parasites" in a television interview on French TV programme Telefoot.
The 32-year-old had accused the pundits of deliberately trying to tarnish his reputation.
The Daily Mail quote Evra as saying: "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," he added. "It won't be these tramps who dirty my image. They must stop lying to the French people."
The FFF have since asked the Manchester United left-back to explain his comments.
An official statement was released reading: “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.”
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