The engine and the cover appear indicative of ABG VAP, who supplied many small builders of mopeds. The single identifier is the curved tubes at the back, most were straight. I need now to match ABG to a curved tube builder.
Those are fair names, but the bend of the tubes is different. The nearest I've found with the ABG-VAP motor is a 1955 Captivante. Trouble is, there were so many of these three men and a dog operations, often using parts from the same pool of suppliers. I am, however, moderately certain it's an ABG from the visible finning.
There is also the possibility that the machine is the result of the widespread practiice of dealers taking a robust bicycle and adding a moped engine to it. The frame most resembles a Peugeot cycle to me, but the style was widespread, so it isn't in any way certain.
Everything is so close; perhaps the original post has a Mistral engne and this has an ABG VAP, or it's the other way round? I think we've got close to it, it now needs an absolute nerd from France to be certain.
Somebody else homed in on your Salmson picture, and I think that's what it is. The only real question left is which engines they used, because there were several maunfacturers. The angular covers I have seen on bikes listed as using the ABG VAP, whereas the curvier panels are found on this Salmson with a Le Poulain Junior single speeder. See this attached link:
The problem with the OP's bike, is it looks like it has parts from multiple manufacturers. Early Moby's used those engine covers, Peugeot (and others) made mixte bike frames with the swoop tail, the rear rack and fender struts appear on different bikes, sprockets match multiple bikes, forks on this bike are bicycle style, not triple tree, etc...
There's not that single identifiable piece that makes you go, "oh! That's it!"
Add to that the hundreds of tiny, obscure manufacturers at that time, and we may never pin it down. For all we know it's changed hands many times over the years and parts were replaced with whatever was laying around, and this is how she sits now. Lonely, ugly, and mysterious.
"this is how she sits now. Lonely, ugly, and mysterious.""
That sounds like some inmates of pubs I go to.
For me, the curve of the frame tubes say Salmson, the 4 hole pulley is typical (not that the hidden engine has to be from the same source) of the Mistral, and Salmson are listed as using both Mistral and ABG VAP. As you say though, not enough to bet the house on.
In the detective work, I've found some odd delights, so the time has been profitably used.