Last year we rented a guest house about 2 kilometers from Mulsanne corner through a outfit called 'Destination Le Mans' and it worked out quite well. Was there 3 nights - you'll find that many places have a week minimum, and I couldn't subject my wife to such a grind. Also rented bikes from the local transpo agency, which were quite handy due to the gridlock traffic you can encounter.

Whatever you do, I am sure you will enjoy it.