I’ve been intrigued by this design ever since I saw it on the cover of a 1977 issue of American Rifleman.
In the 1920s, French inventor Charles Auguste Théodore Levé began patenting designs for magazine-fed variants of the Darne sliding breech side-by-side. One even held four shells in reserve, two for each barrel. Belgian gunmaker Alphonse Forgeron and his successors produced shotguns based upon Levé’s patents, but I do not know if they ever tried the six-shooter variation.
Here is Levé’s US patent: