Corinne Diacre has been sacked as manager of the French national team four months before the World Cup.
Renard released a statement criticising the French “system” and was joined by team-mates Marie-Antoinette Katoto and Kadidiatou Diani in a boycott.
The FFF announced Diacre’s exit and said the situation was “irreversible”.
On Wednesday, Diacre had vowed to carry on and denounced what she described as a “smear campaign” against her.
“I’m determined to carry out my mission and, above all, to do France proud at the next World Cup,” she said.
In their statement, the FFF said a four-person committee had been commissioned to examine the running of the national women’s team following criticism from Renard and her team-mates.
They said the committee had “established the observation of a very significant divide between players” and added the fracture had “reached a point of no return which harms the interests of the team”.
“It appears that the dysfunctions observed seem, in this context, irreversible,” the statement reads.
“In view of these elements, it was decided to put an end to the role of Corinne Diacre at the head of the French women’s team.”
The commission will also be tasked with selecting a new head coach for France ahead of the 2023 Women’s World Cup, which begins in Australia and New Zealand on 20 July.
France are in Group F alongside Brazil, Jamaica and Panama.
The FFF statement also criticises Renard and the players for airing their discontent with Diacre on social media and announcing their boycott of the international team through their personal accounts.
“The committee also noted that the way used by the players to express their criticisms was no longer acceptable in the future,” the statement reads.
Renard, who has made 142 appearances for France, said on social media that she was taking a step back from the team “to preserve my mental health”.
Team-mates Diani and Katoto later announced they would no longer play for France. Diani said the “management” of the team was a reason behind the decision.
Under Diacre, France have not reached a major final and lost to Germany in the Euro 2022 semi-finals.