OP, that Post article is incorrect/unclear where it says, "Those who do not get their application processed in time for their trip must provide proof of a negative coronavirus test taken within 72 hours, regardless of vaccination status." They're talking about the health pass, and they're trying to say, awkwardly, that if you want a health pass, you'll have to get a negative test from a French pharmacy, giving you a 72-hour pass. The Post is making it sound like you HAVE TO to do this, and you don't -- as everyone has noted, you can just use your CDC card if you like.
Per the official diplomatic link, as noted above, "If you are vaccinated, you can travel to France with no restrictions linked to health conditions."