"I ask Gianni Infantino: what message are you sending to the victims of racism, of homophobia, of sexism? As the highest authority, FIFA should apply a policy of zero tolerance," Sonia Souid told AFP on Wednesday.
Several members of the French federation's executive committee confirmed on Tuesday after Le Graet's resignation that he would continue to work at FIFA's recently-opened office in Paris as a delegate to Infantino, the president.
It is a position he was named to in January last year.
"I am going to take over the management of FIFA's Paris office, from next week," the 81-year-old Le Graet told Wednesday's edition of French sports daily L'Equipe.
"It has been discussed with Gianni Infantino. The idea has been in the pipeline for a while."
The newspaper reported that Le Graet had met with Infantino in Paris on Monday, when the FIFA chief was in the city for the staging of The Best awards ceremony.
It added that Le Graet's role would see him work with African national teams, and that he would not be paid.
Le Graet resigned following accusations of sexual and psychological harassment, bringing to an end more than a decade in charge.
His departure came a fortnight after the publication of a damning report into management practices at the FFF following an audit commissioned by the French sports ministry.
"Considering his conduct towards women, his public comments and the governance failings of the FFF, Mr Le Graet no longer has the necessary legitimacy to run and represent French football," the report said.
Souid accused Le Graet of making unwanted advances in an interview to L'Equipe and radio station RMC in January.
"He very clearly said to me in his apartment that if I wanted him to help me, I had to let him have his way with me," said Souid.
Her testimony to the inspectors carrying out the audit of the federation led to Le Graet being placed under investigation for sexual and psychological harassment.
Le Graet has denied any wrongdoing and told L'Equipe that he had been "set up".
On Wednesday Souid responded by telling AFP that she felt she had been "harassed" by Le Graet.
"To hear that my testimony was a set-up, that hurts," she said.
"What have I got to win in this? Apart from risking my career, my reputation.
"Talking about a subject that has hurt me and affected my dignity has only caused pain and suffering," added the 37-year-old.
"Noel Le Graet's behaviour was very inappropriate. What I told the inspectors is that I did indeed feel I was being harassed.
"I was harassed. He needs to accept that."
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