If the cast list on IMDb is to be believed, Marcello Pagliero’s 1950 film Un homme marche dans la ville features an appearance by Pierre Léaud, the film’s assistant director and the father of Jean-Pierre Léaud, as “l’ordonnateur.” While the term has several possible meanings, the only one that appears to fit here is “the undertaker,” which would presumably make Léaud père the small man with the mustache and glasses in the scene linked above (starting around the 1:11:45 mark). Perhaps it’s just a kind of confirmation bias, but some of those mannerisms do look familiar…
EDIT: The video has been removed from YouTube.