Can we travel from UK to France with just a NHS app showing recovery from COVID?

I'm planning to travel with my wife from London to Paris by Eurostar.

I'm fully vaccinated, and hold a French passport. She's also vaccinated, but her last jab was 9 months and 2 days ago, which apparently makes her unvaccinated in the eyes of the French state. She holds a British passport and had covid 3 months ago. Her NHS app COVID 19 record shows a LFT test with a date in March.

Eurostar's page says that unvaccinated travellers can enter with "A COVID-19 recovery certificate showing a positive PCR or antigen test result no older than 6 months"

So does the NHS app count as a recovery certificate?

This French government page says "All French nationals and their partners and children can enter France, subject to compliance with current public health rules."

Does this mean we get to bypass the COVID rules for foreigners, or do we still need tests?

The French embassy in the UK say: "Unvaccinated travellers must present a negative result of a PCR test less than 72 hours old or an antigen test less than 48 hours old before departure (departure of the first flight when the journey includes a connection), or a certificate of recovery (positive result of a PCR or antigen test carried out more than 11 days and less than six months previously."

So does the NHS app count as a recovery certificate?

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 implies that no test in the UK would be valid.