GY, maybe this answers some questions?
At 2 h 10 min 16, the PNF said "so, we’ve lost the speeds" then "alternate law […]". Note 1: The angle of attack is the angle between the airflow and longitudinal axis of the airplane. This information is not presented to pilots.
Note 2 : In alternate or direct law, the angle-of-attack protections are no longer available but a stall warning is triggered when the greatest of the valid angle-of-attack values exceeds a certain threshold.
The airplane’s pitch attitude increased progressively beyond 10 degrees and the plane started to climb. The PF made nose-down control inputs and alternately left and right roll inputs. The vertical speed, which had reached 7,000 ft/min, dropped to 700 ft/min and the roll varied between 12 degrees right and 10 degrees left. The speed displayed on the left side increased sharply to 215 kt (Mach 0.68). The airplane was then at an altitude of about 37,500 ft and the recorded angle of attack was around 4 degrees
This is the important part: "The PF made nose-down control inputs and alternately left and right roll inputs."
The PF did indeed stick the nose down. It didn't work.