Is "demande d’extrait de matrice cadastrale" (https://www.service-public.fr/particuliers/vosdroits/R18819) a right form to request info on property ownership in France? If not - what is? If it is, will it work if only either a reference cadastrale/addresse or personne inscrite, but not both is known? What kind of a mandate is required from an applicant?
The document you are mentioning in your question will only tell you who is paying taxes on a given property, so it might either be outdated or not reflecting the real owner(s).
The way to be sure of the owner of a property is to go to the service de publicité foncière. This can be accomplished remotely or by going to the appropriate office. There's usually a fee associated with these requests. It is unfortunately not clear which of the proposed forms will be required for the purpose of identifying the owner.
See related question here.