We're arriving on the Sunday before the race this year, will there be anywhere open where we can pick up a few supplies? I know the big supermarkets and small family shops are closed on Sundays, how about the likes of the Carrefour at Mulsanne corner?
Intermarche located at Chateau du Loir, approx 45km south of Le Mans, is always open on Sundays up until midday. You could maybe see for other Intermarches on the route from the coast if time is an issue.
Not sure about other Intermarche's for example Le Lude is only open Sundays during July and August. Chateau du Loir is the exception and as you say only up to midday.
IIRC there is a 8-a-huit in Eccomy that I went to in 2010 for bread Sunday morning.
It was definitely one of the small villages on the back roads running South to Mulsanne off the ring road. Had all the usual small supermarket stuff - quite useful.