I've read the BEA report.
A number of things to consider, but I'll sum up the main root cause: the passenger had a medical examination a few hours before the flight, and it followed he got a medical restriction to +3G. Unfortunately, it appeared that this restriction was NOT communicated to the pilot. Whereas he had planned on having a "cooler" flight than usual, just because there was a civilian passenger, he wasn't aware of the +3G restriction, so during the initial climb - which he didn't adapt, because he had no reason to - they were subjected to ~+4G. The report states that the hypothesis of the passenger passing out was rejected, but he got under so much stress that he freaked out and pulled on the wrong thing just as some kind of reflex.
While, my French isn't good enough to understand the full report, there is additional detail in section 2.3.1.1. Mission on page 29.
The accident flight wasn't a dedicated demonstration flight, but a regular operational training mission with three jets in air combat manoeuvres. The doctor telephoned the pilot, telling them to not make the flight too intense for the passenger. The pilot decided to cut the flight short and fly only the first phase, leaving a simple flight out and then returning to the airport.
The takeoff phase was unchanged. Since the accident aircraft was the third one in the formation, it followed the other two in a standard takeoff in order to rendezvous with them later. During takeoff, the pilots do not pay attention to the g-loading, so they may routinely exceed +4g.
Problem with the doctor's communication is again that he failed to mention the 3g restriction. Had it been clearly communicated, I think the pilot would have had a clue as to how to handle the initial climb.
" non communication au commandant de bord et au passager de la restriction médicale à 3 g suite à une
aptitude médicale délivrée avec restrictions moins de 4 heures avant le vol ; "
So the doctor's recommendations were clearly too vague for some unknown reason. This restriction alone should have been enough to decide to switch to just a basic demo flight.
Now of course nothing tells us for sure that the poor guy would not have freaked out anyway. He underwent a medical exam, but was probably not subjected to any significant psychological testing prior to the flight. Note again that the passenger didn't actually pass out, so that was more intense stress.
And then yes, there were a couple technical faults after the incident, but they are not causes. But as I said, it's amazing how the pilot managed to land safely in spite of them.
The recommendations from the BEA after the flight were:
"(...) respecter le délai de 10 jours préconisé par la DCSSA entre la visite médicale et le vol" - which means there should have been 10 days between the medical exam and the flight, whereas here there were only a few hours, probably explaining why some of the info was not well communicated.
"(...)prévoir un vol adapté ou dédié pour l’embarquement d’un passager occasionnel sur avion
équipé de siège éjectable en cas de restrictions médicales." - which means for any occasional passenger with medical restrictions, the flight should be adapted for planes with ejectable seats.
I'm sure again the pilot was meaning to "adapt" the flight somewhat, but was not informed well enough to make the right decisions.