Provides details of the vehicle, including frame number, etc. and whoever is the keeper.
Even just the vehicle information is necessary.
Vehicle documents in countries like Italy will have tyre sizes (with optional sizes as well) so that the police can check everything is up to spec.
It is mostly to identify/verify the vehicle more than just assessing the owner. They normally check that the markings (mostly VIN) is the same across insurance/plate on the vehicle/V5 or whatever documentation exists.
Most times they are not aware that the V5 indicates keeper, not owner. Had to explain a couple of times.
Italy is the same as France and Germany. You have to take with you the (annoying) paperwork*.
Over the years I resorted to always having a digital copy with me of everything. I lost count of the number of times I realised I left the V5 for the car or bike at home while I was already around Dijon.
I've been stopped a few times for random checks I always presented the digital copy and they never said anything. Obviously have your license, proper one, not a copy.
I spend a fair amount of time with my vehicles in Italy generally, and there the fine for not having the documents with you is about 40 euros and then you have to bring the originals to the police within 24 hours.
When there, I leave the V5 in my luggage at home or in the hotel, or wherever and rely on the digital copy if I get stopped.
I've yet to be fined, but I'll gladly pay the 40 when it happens.
Same technique all over Europe.
Been stopped, with the car, in Switzerland ones and I got a bit scared, but they were ok with not seeing the paper copy.
*if you loose the paperwork you have to re-register the car. Ask me how I know.