Dream Land;
The "Alpha prot" mode of the 320 is, of course, beyond the control of the crew but it is automatically disabled below 100' RA.
The decision was made by Captain Asselin to do the fly-past above 100' so he elected to permanently (for that flight only - it re-engages but only after the next landing), disengage the a/thr so it would not "spoil" a high angle of attack, gear-down, low-speed fly-past demonstration by engaging.
The fly-past was actually flown at and below 30' ostensibly because the grass strip was so narrow and so short that height perception made the field "smaller" and so they flew lower. Cockpit planning and discipline issues arise here but we won't be distracted from your question. When it became rapidly apparent to the First Officer first, that they were below the trees, Asseline "firewalled" (to TOGA) the thrust levers and the N1's, which were at about 29% or IDLE thrust, took the expected six to eight seconds to accelerate. They almost made it - another second or so and the airplane would have skimmed the treetops and the engines would have not have swallowed as much foliage. Academic though it may be, to some extent the fbw (yaw damper) kept the aircraft relatively straight as it descended through the trees.
That is the extent of the "intervention" with the autothrust and was never a "computer problem" as so many claim.