Magali, presented in 1908 as a "new" car.
According to several online sources, between 1905 and 1906, Gayon et Cie manufactured motorcycles, tri-cars, and automobiles under the brand Magali. The automobiles were said to be small 'voiturettes' built on chassis provided by Lacoste et Battmann. The puzzle car is presented as new in 1908, and doesn't look like a voiturette powered by a motorcycle engine, so I initially questioned whether is was related to Gayon's Magali brand. However, Gayon et Cie is mentioned in the accompanying article as an exhibitor at the 1908 event, along with a comment on the efficiency of its automotive radiators. So it seems possible that the company produced full-sized automobiles under the Magali brand, and for longer than what is widely stated online.