Yes presumably we're some around 1924-25? By 1926-27 even lightweights were doing away with belt drive and getting a front brake.
Albion boxes of all sorts were advertised in the French magazines of the day, for example in La Revue Motorcycliste et Automobile in August 1925 below, and were used in many French bikes.
Atania is a new one on me. Must have been a very small manufacturer, presumably M. Jean Barbet of Lorient (in the Morbihan district in Bretagne (Brittany), France? Barbet registered the name Atania for his bicycles and bicycle parts in October 1921 - no mention of motorcycles so presumably they came along a year or two later.
I have quite a few books on French motorcycles, but Atania is not mentioned in any of them. Atania was not exhibited at the annual shows in Paris in late 1924 (unsurprisingly), nor did it appear in a comprehensive list of French manufacturers for 1925 in La Revue 10 November 1924.
Based on my experience with small Australian makes, I'd guess that Barbet [edit: not Bardet] either built the bikes from available parts, as suggested by 33d6, or put his bicycle head badge on a machine made for him by someone else.
Speaking of the head badge, I wonder if it was specially made for Atania? Hard to see in the photo, but it looks like it might be a generic badge, onto which you stamped your own brand - in this case CYCLES ATANIA. Are the radial marks to help you line up your letters in a nice arc?
Tell us what you know!
Cheers
Leon