The "American Sniper" star filed a lawsuit against "Oops!" reported Ace Showbiz.
According to a statement which Cooper, 40, filed with the help of French lawyer Vincent Toledano, the actor had never publicly addressed dating rumors with the Russian model.
Under French law, the story clearly violated Cooper's right to a private life as the country bans any publications form printing any information about celebrities' personal lives.
In the lawsuit, the "Hangover" actor is also asking the magazine for 11,000 Euros or around USD 12,500 in damages, in addition to legal fees.
Prior to Cooper, Leonardo DiCaprio filed a lawsuit against the same magazine for making a fake report claiming he shared a baby together with Rihanna.