We’ve just come home from this sort of holiday, we stay in cabins regularly. We took the absolute bare minimum clothing and toiletries with us, as flying with hand luggage only. (Long story, but we travel at short notice on staff standby tickets and have found our luggage is better kept with us than risked in the standby system if we play the staff travel lottery in the school holidays!) We had a great time. They have supermarkets in France, and you can buy absolutely everything listed above (except books in English, your own favourite teabags, and possibly marmite but you can get even that if you are in a big expat area) in the shops. Our cabin this year had a welcome pack with cloth, scrubber, tea towel, little bottle of washing up liquid, 2 dishwasher tablets, a couple of bin bags, 2 loo rolls, hand soap, shampoo bar, as well as a bottle of wine, bottle of fruit juice, and a packet of nuts.
The only items other than clothes, personal toiletries and medication, and books, that we brought with us were beach towels, teabags and a single laundry tablet for a ‘halfway’ wash. There is absolutely nothing I wish we’d brought more of with us, in fact if anything I could have got away with bringing fewer clothes and another laundry tablet. It was lovely on our last day, just packing up 3 cabin bags in minutes and then spending the rest of the morning sitting by the river. We saw several families loading up their cars and roof boxes with what seemed like all their worldly goods. I find it amazing that they were on the same sort of holiday as us, and yet somehow they had brought so much more stuff with them.
But if you want to take everything with you, fill your boots. You’ve got an entire car. Some people like to take their own stuff with them.
Fwiw, posters mentioning taking salt, pepper etc with them - we bought a tub of salt for 39c. We also bought a giant citronella candle that easily lasted the week for €2, tin foil for €1, a huge bag of ice cubes for €1, and bought olive oil, shampoo, suncream, soap, more loo rolls, and the all important (for us!) pack of playing cards with local pictures on whilst there.