Actually the original Cousteau / Gagnan prototype regulator, the Gasone (sp?) was a two stage regulator, so was their first production rectangular bakelite regulator and probably their most important the CG45 (the first to have the same looks as most double hose introduced in 1945) was also a two stage regulator.
The Gasone originally did not have the exhaust hose and therefore it did free flow when the exhaust (at the mouthpiece) was higher than the demand valve diaphragm (mounted on the tank valve). The actual Cousteau Gagnan patent was related to the exhaust location and the exhaust duckbill.
The first single stage regulator was the Over-Pressure DX regulator also design by Gagnan and was introduced around 1955. The single stage regulators (first the Over Pressure DX, then the Stream Air DW, and then the Mistral DW) were the very first regulators to incorporate a venturi flow assist and therefore they actually breathed better than the two stage regulator of the time.
The early two stage regulators (such as the CG45, the original Aqua Lung, the Navy type DA, the Navy Approved DA, etc.) did not have any venturi flow assistance. My understanding is that the DA Aqua Master was the first two stage regulator to incorporate the venturi flow assistance (in 1958).
BTW the first stage in the Gasone looked just like an oxygen welding regulator and Gagnan just attached to it the demand valve second stage. It wasn’t until the CG45 that the two stages where integrated into the single housing we are familiar on vintage double hose.
It is kind of interesting that the latest double hose, the new Mistral actually looks more like the very early Cousteau/ Gagnan regulators and it also basically lacks any significant venturi assistance.