The pope has no authority to choose who is the Emperor. The title of HRE was ostensibly an elective office as defined by the Golden Bull of 1356. The pope attempt to choose an emperor would not only piss off Napoleon it would alienate the German states.
If the Pope looked at the situation as being the Habsburgs effectively abdicating their claim on the title, the Pope has as much right as anyone to PROPOSE a new Emperor to the Electors. Quite what this means if the Electors have all taken kingdoms and Grand Ducal titles from Napoleon in return for giving up their role as Electors is uncertain. It could potentially be argued that the dispossessed religious electors are now the only ones who remain, so the Pope could propose a name to them, arguing that nobody has the right to dispossess them of their role, and they could back his choice.
Why not ask a moderator to move this to the ASB forum.
This is NOT as ASB discussion but a historical one.