The Spanish giants have defended their former player and manager after Le Graet told French television channel RMC Sports that he would not pick up the phone if Zidane called about coaching France's national team.
Le Graet said he did not "give a damn" what Zidane did next after the FFF announced on Saturday it had extended France boss Didier Deschamps' contract until 2026.
A Real Madrid statement read: "Real Madrid laments the unfortunate statements made by the president of the French Football Federation, Noel Le Graet, about Zinedine Zidane, one of the greatest legends of world sport.
"These words imply a lack of respect towards one of the figures most admired by football fans around the world and our club expects an immediate rectification.
"Zinedine Zidane, world champion and European champion defending his country's jersey, among many other titles, represents the values of sport and has demonstrated this throughout his professional career as a player and as a coach."
Speculation over Zidane being a popular choice to succeed Deschamps had been mounting following France's World Cup final defeat to Argentina last month.
Le Graet told RMC: "I know very well that Zidane was always on the radar. He had a lot of supporters, some were waiting for Deschamps's departure... But who can make serious reproaches to Deschamps? Nobody.
"He (Zidane) does what he wants, it's none of my business. I've never met him, we've never considered parting with Didier.
"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."
When asked if he thought Zidane would now be in the running to take charge of Brazil, Le Graet added: "I don't give a damn, he can go wherever he wants."
Zidane, who departed as Real Madrid head coach in 2021, won the World Cup in 1998 and the European Championship in 2000 as a player with France.
The 50-year-old also won the Champions League as a player with Real Madrid in 2002 and as their manager led them to three successive European titles from 2016 to 2018.
France and Paris St Germain forward Kylian Mbappe also defended Zidane after Le Graet's comments.
The Qatar 2022 Golden Boot winner said on Twitter: "Zidane is France, we don't disrespect the legend like that..."