We have done this journey and have found it easier to just book a hotel in the French port (we do Boulogne) and then get an early start after a decent night's sleep. If you don't get to the hotel till 2 or 3 in the morning you will be woken at 7 by everyone getting up and crashing about.

I second Hi De Hi's advice. First of all it's not always easy to find a hotel at night, especially if it's in an industrial area! The driving time you give will bring you to Reims after about 2.75 hours drive and if you REALLY want to stop there for a hotel, the TINQUEAUX region, just at the junction of the A26 and A4 has a large selection of hotels of all quality levels, from Formula 1 upwards.

BUT you might find that your card doesn't work, or that the hotel is full, or ... and it's dark, raining, blowy (yes even in June!!!)

I'd strongly recommend that you overnight in Calais, because you will be losing an hour on the ferry because France is an hour ahead of England and it's much better to sleep earlier and start earlier. After all many hotels provide breakfast from 6.30 ish, and the Ibis chain offer something from 4 am.

Better drive south with the dawn and a good night's sleep behind you, as you come to terms with driving on the 'wrong' side of the road, pay tolls and tackle lorry drivers!!