Cland
How do I know AF447 wasn't deep-stalled? Well, I started by paying attention in high school science classes, which helped me to understand aerodynamics lessons during my flight training. One of them involved deep stall and I learnt it has specific meaning: it is stall which cannot be recovered by conventional means such as actions on elevator, stabilizer or power. While AF447 never fully recovered, mere reduction of power or just moving the elevators towards the neutral (while never reaching it) abruptly decreased its AoA - which is incompatible with deep stall as we know it. Now if your goal is to be taken seriously in discussion, you won't go a long way if you take well established terms and start assigning them just your own definitions.
Absolutely, this was not a 'classic' deep stall as Dozy points out with a high tail sat in the wake of the wing. However, it was a stable stall and almost certainly did not feel like a stall.
Many years ago I can remember playing in a simple single jet reducing to stall speed and then applying power and reducing further and sitting below normal stall speed on the power 'the wrong side of the drag curve'.
What the AF447 incident appears to be was a zoom climb into the stall and flying in that way you will get almost no buffet as you are using kinetic energy to stay up. Then at just the wrong point full TOGA power which holds the nose up keeping the extreme AOA but the power is insufficient to maintain height. So the aircraft now is the wrong side of the drag curve, its THS is nose up, its thrust is pushing nose up, and for a time the PF is pulling nose up. This is a totally repeatable stable stall with the aircraft held the wrong side of the drag curve 'sitting on its thrust' but with insufficient thrust to accelerate or maintain height. Had the PF not been so effective keeping the wings level, the aircraft might have fallen sideways out of it.
As people here have said recovery would be to put everything nose down, engines idle, trim THS nose down, push stick nose down - ideally to 40 degrees nose down or so then as the aircraft speed starts to increase slowly increase power and once the speed is above stall speed pull nose up to maintain 10 - 20 kts above stall speed increasing thrust to cruise thrust. But they didn't know they were holding the aircraft in a stable stall so they didn't even try.
Unfortunately, it would appear that training nowadays does not include anything that gets the pilot to feel how the aircraft behaves at extremes and how to get back. As many have said - the idea is not to get there. Fine - but that means you have to accept the occasional AFR447 when for whatever reason the aircraft and the crew find themselves outside their 'flight envelope' and discuss what could be wrong all the way to the surface. Now, as a fully paid up SLF that idea does not fill me with enthusiasm.