From Wikipedia: "Public figures can be photographed as part of their function or professional activity... A photograph of a public figure taken as part of his private life therefore still requires explicit authorization for publication. Thus, the Prime Minister cannot oppose a journalist photographing him at the exit of the Council of Ministers or during an official lunch, but he can prohibit the publication of photographs representing him at an event in his private life, such as a family reunion.”
https://fr.wikipedia.org/wiki/Droit_à_l%27image_des_personne...
For actual photographs of real persons Denmark and many other E.U. countries already have a broad system of legislation that governs your right to your own likeness. It usually assumes that it would be illegal to take and/or publish an image of a random person in a place/during an activity where they would have a reasonable expectation of privacy (i.e. in their backyard) or that was taken in a manner explicitly designed to circumvent reasonable precautions to ensure privacy.
This is counteracted by the public interest, which can cover certain activities of public persons (i.e. a prominent politician having an affair) or public activities of random persons (i.e. you taking part in a protest march). It's decided on a case by case basis based on quite detailed laws and decades of jurisprudence.