We have had to dash to L/H before and made it in just over 2.30hrs. I reckon you will have loads of time to get there for 1900hrs check in. Just in case you don't....sorry for giving you false hope!!
The best route out by far in our (LADWACACC)opinion, starts by moving your car to parking/camping bleu during sunday pm and watching the end of the race from finish straight. Leave track as soon as they cross the line and head for Arnage Village via the lane that divides camping blue nord from sud, ( the lane is first on your right after you pass entrance to track by Maison Blanche, heading south, away from grandstands). Turn left at the bottom of the lane over the train tracks and you come to a roundabout on the North of the main drag in Arnage; the Bobbies direct you north towards Le Mans city on the westerly by pass through industrial estates. Before you know it you are past Auchan and heading for Le Havre. My preferred route is then on the dedicated autoroute back to the A13, fast and no junctions, a little boring but hey you will have seen the end of the race!
Best of luck
Doug
see map ref: lane is that just below aerodrome. You will need to click 'search' on the Michelin web page.
http://www.viamichelin.com/viamichelin/int/dyn/controller/mapPerformPage?strCountry=1424&strAddress=Arnage&strMerged=&x=42&y=10#