Deschamps guided France to the World Cup, joining Brazil's Mario Zagallo and Germany's Franz Beckenbauer in having won the trophy as both player and coach.
He had already signed a contract extension until 2020 prior to the tournament, and FFF president Noel Le Graet had said that agreement would be respected regardless of what happened in Russia.
Zidane stepped down as Real Madrid boss in May after winning the Champions League three seasons in a row, with many suggesting he would be a perfect candidate for the national post.
But on Thursday, Le Graet said appointing Zidane had never been considered.
"We haven't thought about it. Didier's in place until 2020. Me too. We'll see," he said. "We have a contract until 2020. Even if it had gone a little less well, I had said he would be present until that date. And now we won, and in what a way!
"You don't get anywhere without work. Didier and his staff spend hours watching this or that player, and opponents. There's no improvisation.
"There's sometimes luck, you need a little bit, like a shot going in off a post. But the work carried out by Didier and his team is considerable."
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