I'm sorry, I clicked on this thread hoping to see a picture of a seven month old puppy... I'm disappointed
Unless rules have changed, you'll have to take your pup to a vet in France between 24 and 48hrs before crossing back to the UK. Better double check, although it's been a while since I last did this (probably 11yrs). But as others have said, puppy that doesn't get along with the van, and long trip... not a good combo. My lab had trouble in the first year, but eventually grew out of it and could sleep for hours on end while traveling. I think he found the movement of the car soothing and sent him to sleep.
For shopping, as others have said, get creative. Pack as much non perishables as you can for the two weeks, and use small shops or outdoor markets for other stuff. Will take some planning to find the markets, but they are out there. Here in Switzerland I've never heard of dogs being stolen. It's common for them to be left tied up outside shops, and there's usually even special hooks to tie dogs to. If you do go to Como and go via Switzerland, that's an option, but I'd make it very quick in/out with a young pup.
Certainly don't leave the dog locked in the van, other than for a very fast nip in to the toilet.
But if you happen to find yourself near Zurich and need someone to look after your pup for half an hour while you shop, I'm available
I know you've already booked, but I would have simply stayed in the UK for this first year, and try again when he/she is a little older. Will be easier