There's a lot of speculation to what the messages that were transmitted by the aircraft back to France. A lot of information could be obtained from them as they would be in order of occurance. The ground based software to analyse this is called AIRMAN for Airbus aircraft.
It will give all the cockpit effects(ECAM warnings etc), class 1 and class 2 maintenance messages. Basically if you've ever seen the PFR after a flight thats exactly whats on the AIRMAN system, but in near real time.