Earlier quoted context omitted.
> It's like that everywhere in Europe. Nobody says 'see you at fifteen'. Not really? In France it's perfectly normal to say "Rendez-vous à quinze heures" or "Le film commence à vingt-deux heures trente"
OK, it might be a social construct. I'd never say 'treize heures' to set a time with my Parisian colleagues, and neither would they (to the best of my recollection). Sometimes people would say it, yes, but it'd sound strangely artificial, like read literally from a schedule - which in many cases it would be.
I am not fond of it. It is heavy and in most use cases, doesn't bring more information than 1-12, because the context makes generally obvious to know if we're talking about AM or PM.