No one seems to put much emphasis into the fact that they drove the aircraft directly into an area of severe weather, most non Airbus people convinced that "if only it was a Boeing, with control feedback", etc., etc.
But if we look back at some other aircraft accidents such as the 757 with one blocked pitot tube, this crew did exactly the same thing, other accidents with multiple alarms, completely confused crews.
In the AF accident, multiple alarms and warnings, along with severe weather, brain overload.