France did not have things all their own way en route to the 2018 World Cup, but secured automatic qualification as winners of Group A and are considered to be among the favourites to go all the way in Russian Federation with an exciting young squad.
"Didier for me is the best, there is no contest", said Noel Le Graet, the president of the French FA.
Deschamps also oversaw France's previous World Cup campaign, which ended at the hands of Germany at the quarter-final stage.
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Appearing alongside Jose Mourinho in their pre-Benfica press conference, Bailly said: "Romelu is a great striker". So for me he is untouchable in my team and I think he should be untouchable in support from the fans.
Deschamps, who captained France to their only World Cup title on home soil in 1998, took charge of the team in 2012.
The deal will take the 49-year-old Deschamps through to the end of Euro 2020, meaning he will have been in charge for eight years.
A World Cup victor from his playing days, the former Monaco, Juventus and Marseille coach has been in charge of his country since 2012.
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