Ask the people at CVS whether it detects the N protein. Of course, the person administering the test will have no idea, and will ask someone else (like the pharmacist), who will also have very little clue. I asked someone I know who manages a clinical lab, overseeing hundreds of daily Covid tests, and even she is not sure exactly how you'd find out which tests detect N and which don't.

The good news is that most likely the people checking your test results - airline personnel and/or French border control agents - will also have no clue.

Still, I'm fortunate that there's a local testing site that does rapid PCR at no cost, and apparently all PCR tests are accepted by France.