Mr Optimistic.
They commanded a climb because it was proper to do, at the time, airspeeds were fine. They noted "ALTERNATE LAW" eleven seconds AFTER the a/p quit. BEA haven't said where the THS was positioned at loss of a/p. They do say, however, that the a/c was slow to respond to PF's climb input. "At PITCH +10, the a/c began to climb." If the climb had established at AL snatch, what is the protocol for LAW change?
I do NOT believe the PF intended a climb rate at 7kfpm. Nor do I think he wanted necessarily to climb. He pulled back because what he saw and took in told him a roll left and NU was indicated......let's give them that.
At that point, the 340 zoom might or might not be instructive.
Bottom Line? My feeling is that if at a/p drop and then UAS the pilots were expecting, and given Direct Law, there would be no need to be cautious with the stick, to worry about Protections (or depend on them, falsely).
STALLSTALL at his initial pull? Probably a chirp due his unfamiliarity with the a/c response to his hand, and if he relaxed it, (I think he must have) this was the cause of the a/c lagging in climb response.