Should Popeye be charged with the murder of Charnier?

Of course, Charnier's murder (or execution, or termination, or whatever euphemism you choose) is highly illegal, but the Doyle character exists specifically to commit this type of act which the local authorities would be unable to perform themselves. The real-life person upon which the Charnier character is based allegedly had personal connections to Charles De Gaulle; As a foreigner the Doyle character is morally absolved and politically immune; the Charnier character has been exposed as a criminal and is thus no longer protectable; in all likelihood Doyle would simply be quickly and quietly deported lest a national scandal ensue.
From the standpoint of cinema, the Charnier killing provides suitable, shocking climax on the same order of 'The French Connection', and brings the story-arc to a definitive finale; Doyle has destroyed every other aspect of his antagonist's enterprise, and therefore has only this final act to perform.
From the standpoint of drama, the act is perfectly in character for Doyle, who has endured terrible privation at Charnier's hands; his act is one of vengeance and retribution, which traditionally transcends Law in drama, and especially in film. The murder is morally troubling, just as are the shootings of Nicoli (shot in the back to prevent escape) and Mulderig (wrong place at the wrong time, at least for him) in the first film. Doyle is a morally troubling figure who is 'set up' by his superiors basically as a foreign assassin. This is the central point of the film series, that we, as society, place people like Doyle into these positions, to maintain our moral purity and absolve ourselves of his actions.