Earlier quoted context omitted.
It's definitely a solution when you have an app (assuming you have a 3rd party source of identification of users), but since it's a French key, a sizeable portion of people, mostly elderly, are not using the "official" app but a paper printed QR code that was given to them at the time of the second injection (or a picture of said code). Since the French app is pretty terrible (it used to be the barely functional cont…
Does carrying just a QR code work fine for you? My experience from Germany is that nobody scans the code, they just scroll to details to see there's two vaccinations recorded. This far my QR code has only actually been scanned at the airport.
There is however a prevalent issue with QR code scanning that I noticed twice personally (and friends reported the same experiences at other places), which is that most restaurants use a super cheap phone/tablet with a terrible camera that usually is unable to focus on a smartphone screen correctly.
Once, the person was honest about it and explained they kept having issues with it, and I tried to help him focus correctly his device (QR code size + luminosity seems to be the issue from what I saw).
The second one tried a couple of time, didn't manage to focus and told me "all ok" despite it's device not having scanned me (I could see the screen).
If I had to travel though, I'd definitely take the paper certificate on top of it, as, at least here in France, that's considered for better of for worse the source of truth.