We are of to France this month using the tunnel, on return we are due to arrive back to the eurotunnel late at night, for an early morning train, any overnight parking on site or near the terminal.
There's parking outside the 'Duty Free' shop - but don't know if you can overnight there. You can stay overnight on the nearest 'Aire' (there's one on the Boulogne side of Eurotunnel which actually has electric hook ups on a meter) but no doubt you'll get loads of posts telling you why you shouldn't stay on Aires. Alternatively you could book your last night at either Chateau de Ganspette or La Bien Assise which are both used to early morning departures.