Aye! I took Tarquini down there last year, as he needs a longish run now and again.
I didn't go the "direct" (A1) route from Calis to Paris. I went due South from Calis, parallel with the German border on the "A26/E17".
Eventually I ended up in Paris (though the A26 does carry on South as the A5). I found the A26 a lot quieter than the A1 normally is. It may be worth a punt if you intend to go in August.
It had a lot of "Aires" .. kind of big rest areas. Some have a shop and others just had toilets etc. but it was nice to be able to stop somewhere less busy than the regular service stations.
Paris is a nutter, so best of luck around the Paree-Ferrique. Eventually you come out on the Autoroute de Soleil (A6?) and then it's a fair old tramp toward Lyon.
Get off the motorway towards Bourg-en-Bresse A40 and head East. You'll end up near Mont Blanc' without the need to go through Switzerland.
If you leave Britain on the 07:30 ferry you end up arriving in France at 10am local time. The tramp to Paris takes a couple of hours - the French built it in the wrong place - so you end up hitting it at lunchtime.
It takes AGES to get round Paris.. you won't be on the way South till 13:00 and by then you'll be starving hungry. Go as far as you can as it gets quiet the further south you go.
Don't overdo it though. Have a break every two hours (it more or less coincides with half a tank of gas, so fill up every second stop).
Resist the urge to stop for hours and hours though... nothing knacks your average speed quite like a leisurely lunch break every hour but on the other hand, enjoy the drive.. you're not in some race with the devil.
Towards the south there's a few places that have cheapo B&B facilities. You have to guestimate your average cruising speed and stamina and book one in advance, if it's high season.
Personally, I always use the Holiday Inn after you crossed into Italy. If you make good time you can get through Mont Blanc in the evening and the HI is down the road towards Aosta. It's new, big (lots of rooms) has benzina and is right on the Autostrada.. but reckon on getting there after 8pm. It's still light. but you'll be rubber-ducked.
Bring a cool-box that plugs into the ciggie lighter and put some sandwiches, fruit and water in there, so you have something to nibble every time you stop. Don't do the big lunch after 2pm or you'll nod off. It's better if you have a snack every time you stop.
Put one bottle of water in the freezer before you leave (so it freezes). It'll stay cold all the way to Italy. Don't drink too much fizzy pop or caffeine drinks.. just eat light snacks, have a regular drink of water and good, regular breaks.
Bring something to put under your throttle foot.. a cloth or something (you'll get cramp) and it's an idea to have sunglasses. Wear long sleeve shirt as you'll get a burnt arm otherwise.
Dunno the mileages but I think Calis to Holiday Inn Aosta is about 600miles. It sounds like you only have to average 60mph but if you stop a total of 2 hours, you have to average 75.. you get the idea.
I'll try and find the details for HI Aosta if you think you're up it.