Bradley Cooper -- Sacre Bleu, I Must Sue Zee French Magazine ... Over Irina Shayk

Bradley Cooper's relationship with supermodel Irina Shayk is nobody's business -- at least in France, according to a lawsuit the actor just filed against a magazine there.

Cooper's gunning for Oops! magazine over its May 28 story declaring ... "L'amour au grand jour" ... which loosely translates to ... love out in the open.

In the lawsuit, filed by French legal eagle Vincent Tolédano ... Cooper says he's never spoken publicly about dating Shayk, so the story violates his right, under French law, to a "private life."

It sounds weird in this country, but Bradley might have a case in France where celebrities are treated more like your average Pierre ... at least when it comes to privacy. He's suing Oops! for 11,000 euros.

Interestingly, Tolédano just filed a similar lawsuit for Leonardo DiCaprio against the same magazine for its cover story claiming he knocked up Rihanna.

Oops! tells us it has no idea why Cooper is suing, since their story is based on photos that ran in a Spanish magazine. In fact, those same photos were also everywhere in the U.S.