The PF (Bonin) apparently never became aware of his angle of attack (once the airplane fully stalled, AOA was absurdly high). He did not seem to be aware that his constant inputs had caused the Airbus's THS (trimmable horizontal stabilizer, horizontal flaps on the tail) to deflect to maximum in order to try to keep the nose up. Therefore when he tried to input stick up (nose down) several times briefly, and there was no obvious response (the computer takes a while to reduce THS elevation in response to opposing input), who knows what he thought -- maybe that all readings were incorrect.
Strangely, Bonin was the one pilot who had significant recent glider experience as I recall. The Airbus computer even in "alternate law" functions nothing like a glider (only "direct law" is sort of close to direct input), so maybe that further confused him.
In my opinion, at night, over an ocean, in a storm, with no visibility, in possibly significant turbulance, a modern aircraft cutting off Autopilot for any reason other than computer failure is completely unacceptable. A computer should be able to fly as well as a human under those circumstances.
People suggesting that on airliner forums get flamed. But it's true. Most pilots kept up the refrain that a computer cannot safely fly by gps and gyros unless they also have airspeed. Which is true. It's dangerous to fly if you don't have true airspeed (gyros and gps cannot accurate provide relative wind speed). However, if pitot tubes are frozen and the computer no longer has valid airspeed, the pilots no longer have valid airspeed either. Pitch and power is all they can do. The computer can do that just as well. All it needs to know is aircraft weight, which can be entered (maybe it is entered) before takeoff and automatically adjusted to account for fuel consumption.
There are a bunch of factors that contributed to the accident:
Pitots shouldn't have frozen.
Lack of Air France training for controlling an aircraft at altitude with the computer in "alternate law" (mode without full flight envelope protection; it's therefore possible to stall).
The command structure in the cockpit without the Captain (who had just gone on break) actually had Bonin in command, even though the co-pilot in the left seat outranked him... AF has since changed that. CRM (crew resource management) was poor; the co-pilot in the left seat didn't try to take control until way too late. The co-pilot was preoccupied with where the Captain was rather than offering constructive input on how to fly.
Bonin was not adequately aware of what his inputs were doing, or what the plane's Angle of Attack was, and did not react properly to the stall warning which in almost every case at high altitude means drop the nose, not raise it (though without valid airspeed there's a risk of overspeed which can cause a new set of problems).
The Airbus computers had some quirks; stall warnings stop if airspeed drops too low (due to some computer programming logic involving low airspeed, AOA sensors, and the result being silencing the stall warnings).
Nobody believed a passenger aircraft would be so stable during a full stall. This undoubtedly contributed to confusion about whether they were actually stalled. The Airbus's computer setting the trimmable horizontal stabilizer to max nose-up deflection, in response to Bonin's almost constant nose-up input, possibly contributed to the stability during stall.
Angle of Attack information may not have been adequately displayed to the PF (Bonin) -- the black box doesn't record data from the right set of instruments, so nobody knows what Bonin had on his screen.
There was poor notification on the co-pilot's side of what the PF (Bonin) was doing. Unlike traditional aircraft, it is not easy to see what the pilot in the other seat is doing with the stick.
There was poor notification on either side of the cockpit when the other pilot took control. When the co-pilot took control, Bonin almost immediately took control back, and it's not clear either of them knew what the other was trying to do. Apparently there's a light that indicates override, but who would notice such things under that amount of stress?
IOW, it was a disaster from top to bottom. Usually in aircraft accidents there's a chain of events, but in this case there were so many possible contributing causes that other than having better pitots that didn't freeze over, solving any one other problem may not have broken the chain.