When she discharged her firearm, she intended to kill. That is what police are trained to do in the face of imminent danger. It is too dangerous to try and fire a warning shot or inflict a non-fatal wound to an attacker.
I can't personally rationalize that, were she intending to commit premeditated murder of Jean (much less motive), that this is how she would go about it. There are other possibilities such as crime of passion intentionally confronting him resulting in killing him, but of course this is not the narrative she provided.
The alternative is to believe her story. Personally, as a psychiatrist, I have seen some really bizarre dissociative episodes and acute psychotic episodes, none involving killing someone else, but certainly makes me realize that her story, regardless of all the off details, is plausible. Those are exceptional cases, but if it's the only thing that makes sense, then it's likely the right explanation.
It puts us in an odd place legally and societally if we accept her version of events. One might ponder psychiatric treatment, which of course I couldn't imagine at least a regular therapy wouldn't be important for her, but as far as the psychiatric disturbance that specifically led to this action, it has already resolved.