Lyman,
"He tried the entire while to drop the nose, by pushing the Stick forward".
After lurking and reading the recent posts on this thread, it's time for a reality check. From the BEA Final Report:
Pg.173: Following the autopilot disconnection, the PF very quickly applied nose-up side stick inputs. The PF's inputs may be classified as abrupt and excessive. The excessive amplitude of these inputs made them unsuitable and incompatible with recommended airplane handling practices for high altitude flight.
The chart on Pg.96 showing PF's Side Stick Pitch Position confirms this.
Pg.183: In the first minute after the disconnection of the autopilot, the airplane exited its flight envelope. Neither of the two crew members had the clarity of thought necessary to take the corrective actions. However, every passing second required a more purposeful corrective piloting input.
After autopilot disconnection the nose-up inputs produced a load factor of up to 1.6 g, that is to say 1.4 g if the turbulence component is excluded. Maintaining a high pitch attitude first resulted, when the airplane had sufficient speed, in a fast climb speed (up to 7,000 ft/min) and then a rapid increase in angle of attack. At high altitude, such climb speed can only be achieved by converting kinetic energy to potential energy, that is to say at the expense of rapid decrease in flight path speed.
In addition, the thrust value of 84% N1 was lower than the thrust necessary for level flight (95% N1) due to the reduced mach ordered a few seconds before autopilot disconnection, then changed to "Thrust Lock" mode at 2 h 10 min10. The thrust was readjusted towards CLIMB at 2 h 10 min 23 even though the airplane was already climbing rapidly with a vertical speed of 6,000 ft/min.
These factors induced a rapid reduction in the kinetic energy and brought the airplane above its lift ceiling, at a Mach level at which it was then flying. This rapid exit from the flight envelope was not understood and thus not anticipated by the pilots.
One more time, It wasn't the airplane that caused this...