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.

The woman - a 45-year-old mother of two - was convicted in August along with an unmarried Sri Lankan man.
She was sentenced to death by stoning, while the man was sentenced to 100 lashes.
Saudi Arabia's decision to stone the woman was condemned in Sri Lanka, where protests were held.
Sri Lankan embassy officials visited the woman in a Saudi jail on Sunday, Deputy Foreign Minister Harsha de Silva said.
The country had appealed to Saudi Arabia's government to pardon the couple.
"Through our intervention, they have agreed to reopen the case," Mr de Silva said.
"This is a big victory. We will provide her with legal help."
Deputy minister Ranjan Ramanayake added that the Sri Lankan government was informed about the woman's case only after she had been convicted in August 2015 - despite the fact she was arrested in April 2014.
"Islamic Sharia law says four respected Muslims need to be eyewitnesses for this type of case, but this has not been possible in this case," he said.
"Unfortunately, not knowing the law, she has confessed under pressure without any legal help."
Protests were held outside the UN compound and the Saudi embassy in Sri Lanka's capital, Colombo - with some calling for a ban on sending Sri Lankan workers to Saudi Arabia.
The Sri Lankan government says it is gradually reducing the number of women sent to work in the Middle East.

He was assaulted and had his phone stolen near Regent Road, Great Yarmouth, Norfolk.
Officers were called shortly after 03:30 BST and the scene has been cordoned off while inquiries were being carried out.
The force said the man was being supported by specially-trained officers. Police appealed for anyone in the area at the time to contact them.
Lawyers for France's football manager Didier Deschamps say he will sue Eric Cantona for suggesting his Euro 2016 squad selection was racially motivated.
[NEXT_CONCEPT]
Saudi Arabia has agreed to reopen the case of a Sri Lankan maid sentenced to death for adultery, Sri Lanka's deputy foreign minister said.
[NEXT_CONCEPT]
A man has been raped and robbed in the early hours.