Deschamps, who left Nasri out of his 30-man preliminary World Cup squad, was berated on Twitter by model Anara Atanes, who posted: "F**k france and f**k deschamps! What a s**t manager."
The multi-tweet tirade also accused Deschamps of a lack of respect for the Manchester City attacker.
With France's Cup opener less than a month away - against Honduras on June 15 - Deschamps has now opened proceedings against Atanes, with his lawyer revealing the claim is regarding a 'public insult'.
The French Football Federation (FFF) also backed their national boss.
"FFF condemns insulting remarks against Didier Deschamps and fully supports his coach in his approach," the statement read.
"The unanimous feedback confirmed that the entire France condemned such remarks. FFF believes that the unanimous indignation is enough to condemn such behaviour."
