The Super Eagles reached the last 16 before losing 2-0 to Didier Deschamps' side on Monday thanks to a Paul Pogba header and a Joseph Yobo own goal, both of which came late in the game.
Keshi, who took over as Nigeria coach in 2011, said: "It's time for me to go back to my family and face fresh challenges."
Keshi, 52, has stepped aside before only to be convinced to return, after the Confederations Cup last summer, but is to move on and has been linked with the South Africa job.
"I wanted to leave on a high for my country. Defeat by France was not the right way to go but I'm happy with all I've done for the national team."
In separate interviews at the mix zone, they said they have had their time and would want to concentrate at club level.
Peter Odemwingie said, “I am confident I should go now, and I can say I have no bad feelings. I am happy we played well but lost. I am not too sure now whether to wish we played badly and win or the other way round. Whatever the case, I am happy I am leaving the team in the hands of capable upcoming juniors. They should be held together for a long time. For me I am not getting younger, I need to get home and evaluate what plans I have for the future.”
In response to the fact that he was still young, he said “That is why I was not conclusive. But to tell you, I will like to face club action. I still have three years left in my contract. I will like to stick with the club. I am not discussing any moves. I am happy at my club. For me, I have had a fulfilled time with the national team. I have enjoyed every moment of it. I need to quit now. The upcoming players in the team are good. They need all the chance. I just have to go.”
Enyeama on the other hand apologised to Nigerians for the failure of the team to beat France.
He said, “I want you all to forgive us. You have all done well to support us to this stage.”
NAN reports that Yobo no doubt made history by reaching the 100th cap mark in the national team, indeed the first Nigerian to have accomplished it.
However, he had scored an own goal in the 90th minute – a not so impressive record on a special day in his national team career.
“It happens; it was not really his fault. That should not diminish his contribution to the national team,” Mike Umeh, the Vice-President of the Nigeria Football Association said.