The president of the French Football Federation (FFF) has been suspended following an extraordinary meeting of the organisation's executive committee.
Noel Le Graet, 81, has been under fire since the weekend after saying he wouldn't pick up the phone if Zinedine Zidane called him about managing the France national team.
Vice chairman Philippe Diallo has been named acting interim chairman, according to BFM television.
When he was asked what he would do if the World Cup-winning French football legend was offered the Brazil job, Le Graet replied: "I don't give a damn, he can go wherever he wants."
He added: "He [Zidane] does what he wants; it's none of my business. I've never met him, we've never considered parting with Didier [Deschamps]. He can go where he wants, to a club... If Zidane tried to contact me? Certainly not, I wouldn't even pick up the phone."
Zidane was regarded as a hero after the 1998 World Cup final, which France won by beating Brazil 3-0 at home, during which the forward scored two goals and was man of the match.
The row comes after a successful period for the French national side under Deschamps, who was captain of the 1998 cup-winning side, which has seen the nation reach the final of the last two World Cups - one which they won in 2018 and one that they lost on penalties late last year.
Le Graet's comments have drawn criticism across France with PSG star Kylian Mbappe and President Emmanuel Macron wading into the row.
The FFF president has previously faced claims of sexual harassment, which he denies, and the organisation is the target of an investigation ordered by sports minister Amélie Oudéa-Castéra.