In France this is illegal for at least two reasons:
- health: most people don’t know how to process raw meat or recognize a sick animal (rabies or other illnesses)
- safety: those animals are tough, it’s not uncommon for boars to wake up from the concussion before, while, or after being loaded in a car, and the last thing you want while driving is a wild, fearful, angry animal suddenly waking up and ripping your car apart from the inside while you’re driving (happens).
- law: hunting is regulated so as to control wild animal population growth, killing some has to be reported one way or another.
I suspect there is another historical reason, akin to why you can be prosecuted for attempting to obliterate your own existence: your own being is basically owned by the Republic (used to be the King), so committing suicide is a prejudice to the State. I can see something like this being in effect: wild animals are a property of the State, and killing them even with your car is poaching. That may be why you’re supposed to turn the corpse to the Gendarmerie (cops branch of the military).
(IANAL, correct me if I’m wrong, that just what I’ve been taught as a kid growing in a rural area full of forests)