Poudre S certainly is a nitro powder and not a black powder.
Here is a quote from Edward Chauncey Worden:
"According to Arms and Explosives 1907 the following are the French shotgun smokeless powders:
- J Powder composed of nitrocellulose 83% ammonium bichromate 14% potassium bichromate 3% this being a style of powder in which there is no equivalent in the United States or England
- T Powder is a gelatinized flake powder manufactured from nitrocellulose only of the highest degree of nitration and presumably gelatinized by means of acetone. Cooppal II and Shotgun Rifleite are similar.
- M Powder is composed of nitrocellulose 71% barium nitrate 20% potassium nitrate 5% camphor 3% gelose 1% and somewhat similar to the English 33 cal powders
- S Powder is an equivalent of the English 42 grain powders and the US Sporting Powders and contains nitrocellulose 65%, barium nitrate 29% and potassium nitrate 36%"

So there.

All these powders were made by a government facility which still exists: the SNPE.

"Poudre vive" is a layman term for Nitro. The official wording is "pyroxylee" avec un accent aigu bien sur.
Note that smokeless or semi-smokeless only means that it is not Black.

The 16949 gun on GB shows on its flats that it has been designed and proofed for smokeless powder. This gun was perfectly safe at time of manufacture with the early nitro powders some of which are still available today. As a matter of fact, the individual barrels were proofed once at the proof house with a superior proof (14.5 gram of Black #2 + 75gram of lead), and the finished gun was proofed twice: once in the Manufacture with the 3.46 gram (i.e 53 grains) of powder and 36gram of lead and once in the proof house with or for the S powder as evidenced by the PS mark which actually was developing a higher pressure than the T proof (PT).

The quantity of R guns built between 1898 (beginning of the R model) and 1909 (end of lunette) was probably quite small, and it is not surprising that a Lyon shopkeeper would not have seen any, especially since the majority of hunting weapons vanished during WWII. I know that I have never seen a single lunette Ideal in France, and exceedingly few post 1909 later models.

As for the Manufacture, it was primarily a mail order operation, but this was supplemented with outlets in Paris, Bordeaux, Toulouse, Nantes, Marseille, Rouen, Tours and Lille, thereby covering the largest cities all over France, allowing them to avoid another distribution layer.
In 1924 though, la Manufacture started a parallel retailing channel named "Manumodele" which retailed the "Costo" clone of the Robust. That did not last very long however.
I do not believe that it was ever possible to order a Manufrance model from a regular gunshop before it closed down.

For the afficionados, I think that Manufrance has been restarted and that it is possible to order parts (such as the slings) from regular gunshops this time.

Best regards,
WC