The DD front end looks very similar (closest I've seen)
Yes, I assume the fork is French, or at least continental. "S&AG" rings no bells for me, but I know little about French/continental fork makers. "AG" is (roughly) "Pty Ltd" in German, and often found on German (or Swiss) products. "SGDG" is another commonly seen stamping, relating to patents. I'd actually expected the fork to be AD.
The Dé Dé engines are discussed in the article I posted a link to: Moussard-Madoz (often called just Moussard) and Duten. Try Google translate if your French is a bit dodgy.
The "Bowden France" lever is interesting. Lots of British manufacturers were busy in France in the 1920s, and some like Bowden obviously developed "local" versions of their products. The AMAC brand finished up in the UK c1930 when AMAL was formed, but it continued on from a French base right through the 1930s.
No clear photos of the saddle, but Brooks had a patent protecting the supporting rod to the saddle running through the centre of the spring. Very commonly Brooks saddles have another spring inside, and concentric with, the main spring. If the saddle is Broooks, the Brooks name will be stamped on the saddle clamp, and "10-12 Stone" will be stamped on the front part of the flat steel seat rails. If it's not Brooks, it's a Brooks copy.
All 4 strokes in the 1920s had a cable-operated valve lifter.
Not sure what the object on the saddle post of the Dé Dé and the Claude Delage is, but it might be an auxiliary oil tank. These were sometimes fitted inside the petrol tanks of British bikes, and a measuring cup was used to move the appropriate amount of oil from the oil tank into the petrol tank when filling with fuel, there being no "premix" on offer.
"Zhumoriste" (aka "Bourdache") has written several books about French motorcycles, including one about French motorcycles of the early 1920s) and may be a good person to ask re the Atania. Unfortunately his long-running blog has been disassembled into remnants (like the Dé Dé article) but he now writes at
http://zhumoriste.eklablog.com/ and can probably be contacted there.
Good luck,
Leon