If you want to start rebuilding something, find something that had a larger base stock to work with.
I have no idea why the French needed a 561mm long case for just 700-715mps velocity. Error? Or using different propellent?
The 75mm SA 44 tank gun using the same ammunition as the AA guns used 1270g of BG5 propellant at 2400 kg/cm² pressure to shoot at 715 m/s, while the 76mm M1 apparently used 1700g (3.75 pounds) of propellant at a chamber pressure of 43k psi or 3000 kg/cm². I suspect that the French were just using more conservative loading for the mle.1928 type barrels and could have got more if they wanted. The case was 518mm long. Another example is the 3" M7 gun using a 1920s/30s barrel which offered the same velocity as the M1 using a greater powder charge (4.87 lbs), reduced pressure (38k psi), and lower proportion of case volume filled with propellant.
During overspeed acceptance tests, the loading was 1330g at 2600 kg/cm², and for overpressure tests, they used BSP propellant and reached 2900+-100 kg/cm².
For the 75 mle.97 pattern, in a document related to development of the fortification assault tanks and their armor, it had been stated "the maximum muzzle velocity achievable in a gun with the interior dimensions of the 75mm mle 97 with a projectile of 6.4 kg (under certain conditions). My interpretation is they meant a gun with the same chamber dimensions (same case), but adapted loading and either the same or a longer barrel much like the 75mm M3 with barely lower velocity, while retaining acceptable barrel life. This 640 m/s gun had been approved for the fortification assault tank before going to the 90mm later on.
They got to test a new 75mm capped AP projectile, which perforated a 95mm cemented plate from the Thüringen battleship at 20°, and even 25° for half the shots, at 640m/s (1).
Against a 100mm Schneider naval quality RHA plate, it perforated at 20°, but not at 25° (half-plate deep penetration).
Against 120mm naval quality cemented plate at 0°, it was at the limit of back plate integrity (one spall).
Against 120mm RHA, it only made a 135mm deep dent with a bulge.
75mm mle.1910 couldn't penetrate 100mm plate at all.
Later on, modern uncapped AP analogous to the capped round (same metal as well) achieved back plate integrity limit (light spall) on 120mm RHA under the same conditions, showing the merits of capped and uncapped ammo against cemented and RHA plates. (2)
This is how they settled on 120mm thick cemented plate so that the tank could be safe against uncapped 75mm ammo in similar conditions with "War" rather than naval type plate. The previous 100mm requirement was against the 47mm casemate/mle 37 gun, with 105-110mm actually being preferable to be at full immunity even against back plate damage.
(1) actually lowered by 5 m/s due to the slightly heavier projectile, to keep the same striking energy
(2) velocity increased by 10 m/s due to the lighter round, to keep the same striking energy
I regret not taking pictures of it for later, but one of the archive documents I found was talking about French artillery development and namely what they wanted out of the 75mm replacement before the TAZ 39 happened. For the barrel, they wanted a new quick-change barrel that would be somewhat lighter, would have greater barrel life and would be approved for higher velocities when using AP ammo.
French antitank research in 1939-40 was otherwise concerned with testing articulated self-propelled 75mm mle.1908 (850 m/s) and 90mm AT guns as a hedge against further armor increases, 47 and 75mm self-propelled mounts; a towed version of the 37mm casemate gun (2pdr/37mm M3 level) to replace the 25mm gun in 1941; and a lightweight weapon to assist the most forward echelons of the infantry (many ideas, either an extra-light 25mm AT gun that could be dismantled in a few portable parts, a 20/16mm squeezebore gun, Boys ATR as stopgap).