I have just looked up the registration of Baccarat as a trademark in the UK (often gives European registration) and US databases and it seems they didn't bother to register the name as a trademark until 1969 at the earliest. So that means those marks were never "illegal" and almost certainly not fake. It is possible a decorator used the name to draw attention to his wares, equally it could have been his name or the one he chose for his company. The shame lies more in the arrogance of Baccarat.
The question remains who was Baccarat in the context of these lovely items?
You would be surprised at how many trademarks are ostensibly the same, even within the same category, yet have different owners. It is also not wise to assume that because something is famous, it is trademarked, and also that anything originating from an unfamous company is "fake" because it has the same name as a famous one.