I would suggest the answer to this has already been given.
In 1930 Gangloff built a Bugatti with sliding doors that slid forward. In 1931 he used the same principal on a Talbot drophead coupe which was shown at the Geneva Salon that year. The same year he patented this system of foward sliding doors, and the following year built a second Talbot. The Uhlik-bodied Bugatti took up Gangloff's system but no other cars like this are known.
I know it's impossible to say for certain, but for my money this is the 1931 Talbot by Gangloff. All subsequent sliding door systems of the '30s that I know of used doors that slid backwards. Gangloff's was the only one to do it this way, and the marque and approximate year seem to fit. What do you think?