Cantona said on Thursday that Deschamps intentionally left two players of African origin, Karim Benzema and Hatem Ben Arfa, out of the squad.
"Benzema is a great player. Ben Arfa is a great player," he told the Guardian.
"But Deschamps, he has a really French name. Maybe he is the only one in France to have a truly French name."
He went on to say: "Ben Arfa is maybe the best player in France today. But they have some origins. I am allowed to think about that."
Speaking to French sports newspaper L'Equipe, Deschamps' lawyer called the remarks "unacceptable, slanderous and defamatory" and said his client would sue.
Benzema's failure to qualify comes after he was issued a domestic ban for his involvement in an alleged blackmail scandal over a sex tape.
France's Prime Minister Manuel Valls said publicly before the selection that the Real Madrid striker "has no place" in the team.
Ben Arfa, who plays for Nice and previously played for Newcastle and Hull, is among the reserves for the tournament so could still be called up to cover for injury.
Noel Le Graet, the head of the French Football Federation, called Cantona's allegation "ridiculous."
Cantona and Deschamps, who are former France teammates, have fallen out numerous times since they played together in the mid-1990s.
Cantona has previously called Deschamps a "muppet" and a "vulgar water carrier", a football insult implying Deschamps was good only to pass the ball to others.
Cantona was dropped from the French national team in 1995 after he attacked a fan during a Manchester United game with a kung fu-style kick.
He never played for France again.
Lawyers for France's football manager Didier Deschamps say he will sue Eric Cantona for suggesting his Euro 2016 squad selection was racially motivated.