brunos

I would be delighted to know any lab that would get the results in English and able to use a format that complies with some country requests (like have full name and passport number).

Note that the english requirement is getting widespread. Outside of EU, countries typically ask for tests results in their local language or in English.
I know that this is not a priority, but with the rapid growth for PCR test request when traveling, France should adapt.
I would also assume that labs will have to show Government accreditation as requested by several airline.

Note that there have been many reports and suspicions of fake test reports. This seems widespread in India. That means that many countries will keep imposing test on arrival on top of pre-departure tests.