I live in France but travel back to UK 6 or 7 times a year via Eurotunnel.
As others have said France really is very dog-friendly. They are allowed in most restaurants and hotels. Some hotels will charge a small fee but many “independents” do not.
Eurotunnel is really good for dog travellers. Just make sure you have all the paperwork to hand and allow 30mins extra before check in.
Dogs can go on French trains but you will have to buy a ticket for him. They should also be muzzled but I have never seen this enforced though I do carry a small nylon one with me just in case.
Dogs should be restrained in the car. You can use the full harnesses that are available or you can get a short lead that has a seat belt clip on one end. They are about 3€ from supermarkets. Again, I’ve never been asked for one but have one in the car just in case I get stopped.
Finally, be careful if you are walking around farmland. Farmers, very understandably, really do take a dim view of dogs off leads that “worry” their stock. Also be aware the the Chasse is in full swing at the moment which can mean packs of 20+ dogs chasing through farms and along the chemins.
If you have any other specific questions just ask and I will try to help if I can.