On the route out of the city northbound on the D338 (formerly N138) where it crosses the autoroute, there is a whole gaggle of cheap-n-cheerfuls, including the Hotel B&B, Brit Hotel, Formule 1, Fasthotel, 'Quick Palace' and others.
There's a Premier Classe budget hotel out near the university (a bit further away than that recommended by Big H) but the tram system is also easily accessible from there. I reckon it's a about 10 minute drive to the circuit when there's no race traffic. Have used it a couple of times. Basic facilities but clean. No problems with a late check in as you just book ahead online and use a code to access the premises whenever you like. I cna't vouch for cots etc. but maybe worth a quick look online?