So as I said, the French Tous Anti Covid app now accepts QR codes provided through the NHS App. It's a little bit of a faff to do it on your phone since the QR code scanner won't let you feed it a screenshot so you'll need two devices (I'm using Android, but it looks like the scanner is built in the app so it probably is the same on iPhone).
The app seems to want the second jab code first. If you accidentally add the first dose code first, go to My Wallet, click on the 3 dots next to the certificate and then Delete this certificate.
In the NHS App, once logged in, click on Get your NHS Covid Pass, Continue to accept the T&Cs, and then on Travel (the Domestic ones won't work). There should be a screen with a green tick saying you have records.
From there, swipe to your second dose and take a copy of your QR code.
Once you've installed the Tous Anti Covid app, there is a button at the bottom of the screen saying Scan a QR code.
Scan the NHS code, and you should get a confirmation screen with confetti flying on your screen. I can't get back to it to take a screenshot but you'll know it when you see it.
You can then add the code for the first jab if you want to by clicking add a certificate in the my wallet page.
At the moment, the French "pass sanitaire" is valid 7 days after your second dose (28 days for a single J&J), but it may be different for entering other countries still requiring 14 days.
To view the status on the app, click on Open My Wallet on the home screen, and then click on the certificate. It should open a window (and make your screen as bright as possible) showing the QR code used to enter restaurants and other venues. There's a sliding button to switch it to "Border mode" which will show the date of your second injection.
Et voilą !