Coach Corinne Diacre says she has faced a “violent and dishonest” smear campaign designed to unsettle France before this summer’s Women’s World Cup.
The World Cup, co-hosted by New Zealand and Australia, starts on 20 July.
“I’m determined to carry out my mission and, above all, to do France proud at the next World Cup,” said Diacre.
France are in Group F alongside Jamaica, Brazil and Panama and start their campaign on 23 July.
Renard, the 32-year-old defender who has made 142 appearances for her country, said she was taking a step back from the team “to preserve my mental health”.
Team-mates Kadidiatou Diani, 27, and Marie-Antoinette Katoto, 23, later also announced they would no longer play for France.
Paris St-Germain striker Katoto said she was “no longer in line with the management of the France team nor the values it promotes”.
Former France defender Diacre, 48, took over as manager in 2017 and has made a number of decisions in her tenure that have led to controversy.
In 2017 she stripped Renard of the captaincy – before giving it back in 2021 – and in 2019 she left Katoto out of her World Cup squad.
“I have been the subject of a smear campaign that is astonishing in its violence and dishonesty,” Diacre said in a statement issued by her lawyer.
“My detractors have not hesitated to attack my personal and professional integrity, without bothering with the truth, four months before the World Cup.
“I will not let myself be affected by this destabilisation operation, which does not take into account my sporting record, and which has as its sole objective a personal settlement of scores.”
Under Diacre, France have not reached a major final and lost to Germany in the Euro 2022 semi-finals.