Renard had been in charge of Saudi Arabia since 2019 and led them to qualify for the 2022 FIFA World Cup in Qatar.
Saudi Arabia claimed a memorable 2-1 win over eventual champions Argentina in the group stages but subsequent defeats to Poland and Mexico saw them exit the competition at the first hurdle.
Renard will be named new manager of Les Bleues in the coming days to replace Corinne Diacre ahead of this summer's Women's World Cup in New Zealand and Australia.
In a statement on social media, the Saudi national team said: "The Saudi Arabian Football Federation Board of Directors has agreed on the contract termination of the Head Coach of the Saudi National Team Mr Herve Renard upon his request.
"A legal settlement has been reached to end the contract between the two parties.
"The President and Board of Directors of SAFF wish for Mr Renard every success in his future career."
Renard oversaw a 2-1 friendly defeat to Bolivia on Tuesday and later posted on social media: "Having been the coach of the national team of Saudi Arabia is a great pride for me.
"Since August 2019, I had the chance to be an integral part of the life of this beautiful country. I have seen this team grow alongside me and achieve a fabulous World Cup and this fantastic and unforgettable win against Argentina.
"Very proud to have been able to show to the world the progress and a good image of Saudi football. It's time for me to fly to another horizon but with these memories engraved in me."
Renard has previously led Zambia and Ivory Coast to win the Africa Cup of Nations.
France are in the same group with Brazil, Jamaica and Panama at the World Cup.
