From Memory Alpha:
Rushing to a Jefferies tube, Picard sees a crewman begging for help as Borg technology starts to take over his body and, believing he is saving him from a worse fate, shoots him dead before escaping into a hatch.
The crew member, although infected by Borg nanoprobes and losing control of his body is not yet under control of the Borg, therefore still human. Would the Federation/Starfleet consider it a crime that Picard killed him while he was still human?
What got me thinking about this was a Boston Legal episode where a death-row guard is accused of murdering a prisoner undergoing a botched execution. The prisoner is convulsing from the drugs that are supposed to sedate and kill him, so the guard shoots him once through the head to put him out of his misery. Did he act humanely? Yes. Was it legal? Well...
What if the crew member had been shot in the stomach and would die agonisingly over the course of two hours? Would Picard be justified in killing him then? As the audience we can somewhat see Picard's position and agree that he thought he was acting humanely, but Picard was also rescued from the Borg and had his humanity restored, so he of all people should know that the situation was not hopeless. I think in the ST:TNG era euthanasia isn't acceptable either. I remember an episode where Worf wanted to commit suicide after it looked like he'd be paralysed for life and there was much discussion about it.
So I'd like something more than just "Picard's a good guy who went through some really heavy stuff and we all like him". If he was tried in Boston Legal they'd get him off under temporary insanity... Also how would the letter to his family from his captain look? "Sorry about your son. I had to kill him because he was turning into a Borg. Jean-Luc Picard, Captain, Enterprise"