I came back from France about 10 days ago and while I can't comment on cross border checks within the EU as I didn't do any, my experience in France was not quite the same. Getting into France from the UK only needed an 'honesty declaration' - a form you filled in on line saying that you didn't have Covid. French passport control at Dover wanted to see it (not trusting my phone I had a paper copy).

Hotels / supermarkets /motorway services etc were not bothered about Covid status - you could book them / walk in and out etc and nobody was bothered - as long as you were wearing a mask. I was 'reminded' a couple of times when I was browsing in some smaller shops and forgot to put a mask on. Cafes and restaurants however wanted to see your French covid passport before they'd let you in. No UK stuff worked on their system and no QR code on your phone meant no entry. I didn't find a single cafe that didn't insist on the code before letting you in, and as I didn't have one it meant no leisurely lunches etc The only exceptions were restaurants in hotels you were staying in - breakfast mostly.

Coming back to the UK needed a test done within two days of your arrival at Calais. Finding a test centre locally (near Grenoble) wasn't hard with a couple of them operating a no appointment needed, just walk in, schedule but the test I used came with me from the UK. You buy it in advance, take it with you and email the company to make a Zoom style call on your phone at a suitable time. They then watch you taking the test in real time, and you hold the test strip up to the camera so they can see if it's positive or negative. If you pass they email you the cert. That worked perfectly via 4G on my phone (much to my surprise!)

You need the cert to fill in the passenger locator form, something that only have been devised by a bureaucrat with too much time on his hands. It assumes you're only visiting the UK and wants (amongst other things) to know when you're leaving. The on line version won't take nonsense answers either so it took a while to find made up answers it would accept. Trying to fill it in came close to causing me to miss the ferry. Much to my surprise it wasn't immigration that wanted to see it but the ferry co. Presumably they get fined if you don't do it.

I never heard anything from track and trace - the form is supposed to put you on their radar, but I was talking to someone a few days ago who had also come back from a euro bike trip at about the same time. He got home late in the evening and had someone from track and trace banging on his door at 7.00am the next morning. He was told where to stick his form in very short order