Cantona had accused his former international and club teammate of racial discrimination in his choice of players for Euro 2016, claiming Deschamps had snubbed Karim Benzema and Hatem Ben Arfa because of their "north African origins".
"It's unacceptable and I won't forget, I have made judicial arrangements and I'll go to the end," said Deschamps.
"To hold it against him is the least you can say, I can't forget. I'm a coach, I'm ready to take blows from everywhere. After that there is a limit that cannot be crossed."
Cantona's comments caused uproar before the European championships, where the hosts eventually lost in the final to Portugal.
"One thing is for sure ? Benzema and Ben Arfa are two of the best players in France and will not play the European Championship. And for sure, Benzema and Ben Arfa, their origins are north African. So, the debate is open," Cantona told British daily The Guardian in May.
"But Deschamps, he has a really French name. Maybe he is the only one in France to have a truly French name. Nobody in his family mixed with anybody, you know. Like the Mormons in America."
Cantona, who won 45 caps for France between 1987 and 1995, has in the past been very critical of his former teammate Deschamps, who in 1996 he branded a "vulgar water carrier".
The former Marseille and Leeds United striker retired in 1997 before taking up a career in cinema. In 2007 he married Franco-Algerian actress Rachida Brakni.
The exclusion of Benzema, of Algerian descent, followed his implication in an alleged attempt by one of his friends to blackmail international teammate Mathieu Valbuena over a sex tape.
Ben Arfa, of Tunisian origins, had been hopeful of making the squad after relaunching his career at Nice but instead had to settle for a place on Deschamps's standby list of eight players.