I shall take on Cland here, not as much for honor, but for experience and no small amount of aero knowledge for a "dumb fighter pilot".
Hey, I never called you dumb... or for a moment thought you were. Actually, I find your contribution to thread very valuable.
The thing is programmed to hold a gee!
We had this discussion before; maintaining one local gee when straight and level is consequence of chasing the stable flightpath, not the principle on which system is based. For pilot, difference is most of the time negligible.
I do not believe that the jet becomes unstable, only that there is an AoA and cee gee combo that enables it to reach a stable, stalled condition that we did not realize was possible.
Sorry, I have mistakenly believed you have referred to the part of the final report pointed out by Retired F4 and rgbrock1; that FBW makes the Airbus behaviour slightly unstable by maintaining the flightpath with the speed changes while you were talking about post-stall stability. Flying at such a high AoA was outside the certification scope, as it is assumed that pilots will recognize the stall promptly and initiate the correct recovery action so no one has ever tried to reach extreme AoA in test flight. However, from DFDR data it can be seen that aerodynamics were not enough to keep AF447 stalled; at about 2:11:45, THS is winding up and is 2-3 degrees shy of full nose up, elevators are fully nose up, as trust levers get retarded N1 goes down and nose drops from +15° to -10°.