Hi Gavin,
I agree with the "La Fleche solution", it's easier to access to the circuit.
Use your own car is not a problem but forst please secure your car pass.
Best is parking Blanc, because it's the nearest. But Bleu and Rouge are quite near too.
You don't need to use the motorway from La Fleche to Le Mans, but you can use it from Calais/Le Havre/Caen to La Fleche if you don't mind about the pleasure of the RN138 (a definitely Le Mans' experience pleasure)
They're some hotels still available in Le Mans and you won't need your car as there's an efficient shuttle service night and day from the city centre to the main entrance of the circuit.
Keep in touch for any other questions to make your first LM trip the greatest days of your life !!!