Yes, that's the car!
It is, as you say, almost identical to the Antem car with just minor differences in the window shapes. But that doesn't seem to be unusual with these Delahayes and I wonder if the coachbuilders were given a 'standard' design and asked to make the body, just with some minor changes to differentiate them from the work of other coachbuilders.
I don't have the date either, but I thought the solver might be able to come up with it.. Certainly it is 1951 or 52 so let's call it 1952!