what if he were actually to die while you were in French airspace ? Legally, this is tantamount to dying in France;
According to a book I read (Air Babylon, I think) so this must be 100% copper bottomed fact because it wasn't on the internet, the airlines normally arrange for the death to occur just before the scheduled landing, which avoids all kinds of complications. Obviously this could be done only if the passenger is obviously dead when discovered. If he is just ill then you divert somewhere.
Legally (not a lawyer) it's pretty obvious the pilot cannot be personally liable for the sick passenger - if it is a proper air ambulance flight. The medical staff involved must carry the can for that, with insurance etc.
I would never do it solo.