It would appear that there is more information regarding the last 4 minutes of flight than has been discussed. I am not familiar with the systems of the Air Bus airplane, thus cannot comment with any authority on the alerts transmitted to AF maintenance. But I do have questions relative to them.
Taking each transmission on its own merit, what would likely have had to occur to trigger the first automatic ACARS alert.
Then, would each subsequent alert be a result, or a contributing factor, of a failure reported by the preceeding transmission.
Following the transmission trail and analysing the fault(s) should provide somewhat of a picture of the work load being placed on the crew, and the potential conditions which existed in the cockpit at the time.