If you understood Airbus systems, and there is no talk of them not working in this case, the first nudge of the stick would have disconnected the autopilot with accompanying aural warning and a change on the FMA. Apparently these were not noticed. The reason the CM1 could not disconnect the autopilot was because it was already disconnected.
The first action in a suspected sidestick problem is to hand control to the other pilot, who when he takes it presses the sidestick priority button to disable the other sidestick. The "dual control input" call out shows that this was not done.
The aircraft established controlled flight all on its own despite the best efforts of the pilots. They then recovered the flight path setting power and attitude, not wrong in itself, but indicative of them not recognising what the aircraft was doing, despite the aircraft telling them.
Of course this is pure speculation, but the behaviour of the aircraft, as described here, is what would happen in these circumstances if all the systems were functioning.