score:5
The closest thing to the Première Classe hotel chain in Italy seems to be the BB Hotels chain. There are 23 of these across Italy (mainly Northern Italy), mostly located close to the Autostrada. Prices can be as cheap as those of Première Classe hotels, and, outside of manned reception opening hours, automated check-in is available.
Another option are UNAWAY hotels, which are also scattered across Italy. Some of them are close to the Autostrada. Prices are more expensive than BB Hotels, and automatic/24-hour reception will depend on the hotel.
As @GayotFow points out, there are sometimes motels/hotels adjacent to Autostrada exits, and often these are advertised on the Autostrada. Luckily, there is a website which allows you to search for them. The best way to go about this is to use the drop-down menu on the right on the homepage (the rest of the website is definitely not designed for UX):
If all that fails, try querying your favourite search engine for motel autostrada.
Upvote:2
The International Ibis chain is only a little above that, probably right there for their Budget line.