When are you coming to Tuscany? Game season is highly regulated and goes from September through end of January.
Special licenses are needed, which are not that easily to get. They require a trip to the Carabinieri as far as I know as well, so it might be very difficult for you to even try to get the right license, aside from coming in the right season. Hunting is mostly only allowed on special reserve areas since there aren't that many wild birds or game nowadays.