1901 Parisienne?
I have just discovered a French brand that I have never heard of previously, but which fits all of the puzzle criteria thus far defined, except for the brand(s) of engine used, which are unmentioned. There is even a lengthy article regarding the unusual means of control (clutching, shifting, braking, etc.), as well as a photograph, which, although from a different angle, seems to match the puzzle car. So, is the puzzle car a: Mégy from about 1901 by the firm L. Mégy of Paris, which operated 1901-1903?