From 2 h 10 min 05 , the autopilot then auto-thrust disengaged and the PF said "I have the controls". The airplane began to roll to the right and the PF made a left nose-up input. The stall warning sounded twice in a row. The recorded parameters show a sharp fall from about 275 kt to 60 kt in the speed displayed on the left primary flight display (PFD), then a few moments later in the speed displayed on the integrated standby instrument system (ISIS).
At 2 h 10 min 16, the PNF said "so, we’ve lost the speeds" then "alternate law […]".
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.
My read of the above is that the plane was flying fine when the autopilot/thrust kicked out due to unrelaible airspeed. No power changes are mentioned by the BEA so the thrust required for level flight at FL350 and 0.8 must have been set and being produced. The initial control input is nose up (and left roll) and a climb begins. The plane isn't stalled at this point as a) it's capable of a climb and b) the BEA confirms that the last 3m30s were in a stalled condition which puts the start of the stall at about 2h11m (the stall warn triggers again at 2h10m51s). There are some nose-down inputs mentioned at this point and it seemingly controls the climb but is still probably in a climb (and bleeding airspeed) due to the pitch and VS indicating +700ft/min.
It appears that there was a trade of speed for altitude but no actual stall until 2h11m.
Once the stall begins, all BEA references are to nose-up up inputs and the THS rolls to full nose-up. Some references to nose-down are made later but as others have commented, with full nose-up THS it's a good question how recovery would be made at that point.