The TousAntiCovid app was launched in October and is a free download in seven languages, including English.
The Guardian reports the app has become the first in the EU to contain test results on mobile phones, and that from 29 April it will also carry vaccination certificates.
Those taking a Covid test in France will receive a text or email giving them access to online documents that can be downloaded or printed. Past vaccination and test details will be downloadable from mid May, the paper said.