Upvote:2
This French government page says that you can get a travel certificate - required to cross borders - with "A certificate of recovery from COVID-19: a positive test conducted in France between 11 days and 6 months prior."
This is to get, on request, a EU DCC (Digital COVID Certificate) at a French pharmacy, and is not mandatory to enter France.
The only use in force for the EU DCC as Passe Sanitaire is to enter hospitals, doctors office and other health-related offices as a visitor... source
The only page that is of use to you is the Ministry of the Interior one
While the ideal is to get a paper version of the positive test, the NHS App showing the postive test with the date should work fine