If like me you like to watch the finish at the start/finish line and then join the crowds watching prize giving, you might find this a better route away at the end of the race.
Getting out of the many campsites can be fraught with delays, especially when many multiple campsites feed into a single exit.
An alternative is to pack up and move your car out of the campsites, but instead of Mulsanne, I suggest moving to the Carrefour Hypermarket car park situated on Avenue Georges Durand a couple of hours before the end.
The supermarket is closed on Sundays, however the petrol station there is open as is the covered car park, where you can leave your car. (You could leave it beside the road if you are worried about car park clamping, but this, to my knowledge, is not a disease that has spread to Le Mans.)
The Carrefour is a couple of stops up from the circuit, but it's only a few hundred metres to south to Tetre Rouge and an entrance to the circuit, so an easy walk.
After the finish and prize giving, you can meander up over the Dunlop bridge and out of the circuit and back to your car, perhaps taking a coffee and slice of cake at the patisserie Bouvet Jean-marie just before the Carrefour.
Remembering that the main traffic delays are to the west of Le Mans, travel south and east.
I would suggest travelling south along Avenue Georges Durrand/D338 until the junction with the D323 ring road which you can take going east (unless like me you want a drive up the Mulsanne Straight on the D338 which should be open by then). Drive 8km along the A323 before taking the A28/A11 to Paris/Rouen/Nantes/Rennes/Tours and then join the A28/E502 still signposted Paris/Rouen...... After 5km take the A11 signposted Rouen/Caen/Alencon and away.
Aricus