Thanks for the point Gerd! I was beginning to despair on this one.
I had considered the Baudier early on, but dismissed it for the following reasons (among others).
1. My reference says manufactured in Paris, not Neuilly. However, when you said that you had a reference giving Paris, not Neuilly, I reconsidered it after I ran out of Neuilly possibilities.
2. My only photograph of a 1900 Baudier shows completely different rear seating, and a slanted (not vertical) steering column.
3. I had convinced myself that I saw a chain, or belt, drive in the puzzle photograph, but my reference said the Baudier had a shaft drive.
However, I was getting desperate, so when you said there was one example in a museum, and I had no information regarding a museum for any of my few other possibilities, I went back to review the discards, and decided to try the first one that I found that mentioned a single museum car: Baudier.
So, yes, the museum clue was helpful, but it was still a guess, albeit an educated one.