Shuttle is s good option but if you can afford the tickets that allow lounge use and priority boarding, it is worth it in the summer, as the queues can be really long and sometimes you get bumped and bumped waiting to board. With priority boarding you just get waved through. In the lounge you can feed the tribe easily, use the loos, and pick up magazines for on the way. It is possible to upgrade a Tesco voucher booking to get priority boarding by paying extra.
I always have lots of cleanup things in the car after a couple of truly memorable vomit-related incidents, including the 2007 Aldeburgh explosion and the 2011 Brussels norovirus moment, not to mention the 2004 Centre Parcs queue diarrhoea spectacular. There are professional-standard sick bag kits with wipes and absorbent pads, things that look like bin bags that you put clothes into and then you put the whole thing with the bag into the washing machine, lollies that kids can suck that help get rid of nausea, and little packs with toilet paper and a soap leaf suitable for French service stations where there aren't things like that available. Try these people:
Purple Turtle
I also put water bottles in every door, along with a pack of tissues.
I prepare a travel kit for each child with a juice carton, packet of raisins, colouring book, coloured pencils, magnetic puzzle, little games, child-friendly map of the route, etc. They also all have a travel pillow and a little blanket. I have spare clothes for each child handy in a special bag, along with a jumper/cardigan.
I also like to stop every two hours and let the kids stretch their legs, as this reduces restlessness and whinging by about 50%. Epernay is a good place to stay overnight and less busy than Reims. I have stayed in this hotel and it was economical and comfortable with a nice bar. Ibis Epernay Centre
The French aires can get busy in August and if there is a service station there the queues for coffee can be crazy, so I try to have a flask with me for a quick fix if necessary.
Finally we always have a pretty well stocked first aid kit permanently in the car with things like: ibuprofen, calpol, Solpadeine, insect cream, ibuleve gel, antiseptic cream, dressings, crepe bandage, nit comb, threadworm tablets, antihistamine tablets, ammonium, decongenstant tablets, rehydration solution, etc. It's like Breaking Bad in our car but it saves driving around looking for pharmacies when you would rather be doing something else.