Sorry to spoil the fun but I think I found the car, a bit by luck I must admit.
I was going through a list of slightly obscure French manufacturers when I came upon Ariès, a brand I did not know much about. Checking on the last models manufactured by that company I did a search and found the picture of that very car.
So it is an Ariès "Super 10-50", capable of 120 km/h (74mph), manufactured from 1934 to 1936. I could not find a precise date so I guess it must be from 1936. There was no mention of who did the body.