Well the maiden passenger flight of the A320 crashed at the Paris Air Show, and the pilot said the fly-by-wire system didn't let him pull up[1]. Officially it was pilot error though.

There have been nearly 1,400 fatalities with the A320, with some pilots blaming the fly-by-wire systems, but many of those happened before the age of Twitter and social media virality of this sort of thing so who knows what the public reaction would be today.

[1] https://en.wikipedia.org/wiki/Air_France_Flight_296

The A330 had some weird pitch down incidences due to a faulty ADIRS, and obviously AF447 due to faulty pitot tubes and the completely idiotic issue where the control sticks aren't synced and the inputs are averaged out before being sent to the plane. There were some considerations given to grounding the fleet, whether or not Airbus wanted to admit it at the time.

https://www.reuters.com/article/us-france-plane-denial-sb/ai...

There are several pilots who've had this very issue happen to them and they managed to diagnose and address the problem without flying the plane into the ground.

These incidents are almost always the result of a combination of errors ranging from negligent engineering and documentation to mechanical defects to human (pilot) error. We simply don't know all the facts in these two crashes.

The publicly available information to me indicates negligent documentation (pilot manuals should have been updated to reflect the new mode and how to treat the issue similarly to runaway trim), negligent sales practice (the AoA disagree feature shouldn't be an option), and poor reactions by the pilots involved. But that's purely speculation at this point: there could very well be some other causes instead of or in addition to these.

Air France Brazil to France flight.

Is that a serious question, or did you just not do any research? Yes, Airbus planes have crashed due to malfunctioning automation. It hasn't even been that long since one of their newest planes actually experienced a problem eerily similar to the 737MAX issue, but got lucky in that it occurred when the plane was higher and had more altitude to trade for time and the pilots were able to regain control.