I just returned from France, visiting Paris and (by rail) Provence from December 18 to 26. Here are my notes about the (unromantic) logistics of our trip, in case of interest to those preparing to go to France:
1) On the way to France we had our COVID papers (proof of vaccination and recent test results) checked only once in transit, and that was by an airline official as soon as we entered the airline terminal at our point of origin in the U.S.
2) In Paris there are pharmacies all over the place that test tourists and locals for COVID, and that give you both printed and emailed copy of the results. They often advertise this with big, loud posters.
There are also little square tents set up all over Paris on street corners and in plazas for providing COVID tests; but I don't know if those tents provide tests for tourists or merely for locals, as I was tested in a pharmacy.
Indeed, I found three Paris pharmacies that provided rapid COVID testing on Christmas Day, which in my case was necessary because our plane departed on the morning of December 26. In fact, the pharmacy I used was located in the train station through which we returned to Paris from Provence. It was quick and easy.
3) Every restaurant in France asked to see our French COVID cards. Also, the Louvre and other major indoor tourism sites asked to see our French COVID cards.
4) In one instance a member of our group accidentally showed his U.S. COVID card, not his French COVID card, and it was immediately accepted as sufficient proof.
5) I planned our trip meticulously and so printed out in advance all U.S. and French forms their respective governmental websites said were necessary for traveling . . . and yet never did anyone ask for those forms! Today as I was cleaned out my carry-on bag I found them and threw them away, entirely unused.
Also, on the U.S. government website, and on the U.S. airline app, appeared a claim that all travelers must download and fill out a certain form in order to return to the U.S., and that this cannot be done until 72 hours prior to your flight home : THIS FORM ALSO WAS NOT REQUESTED BY ANYONE ON THE WAY HOME TO THE U.S.!
This being said, I was twice giving a form (different from those I mention above) to fill out by the airlines, once on the flight to France and, later, while in line at Charles De Gaulle airport for the return trip home. They were relatively short forms, and in one instance I only had to fill out one form for our entire group (not one form for each member of the group).
6) Just about everyone in France wears COVID masks indoors or outdoors -- except for a group of anti-maskers/anti-vaxxers I saw marching down a provincial street . . . a harmless, even merry group of about 30 protesters, some of whom banged drums, one of whom spoke through a megaphone, and yet another of whom waved a Che Guevara flag. Interesting. (I took photos.)
So, to summarize, the French and U.S. governments clearly take the COVID threat seriously, and do indeed want to see your U.S. and/or your French COVID cards and test results. But all the forms mentioned on both the U.S. and French government websites as "necessary" turned out to be unnecessary. This being said, my experience might differ from yours and so I suggest erring on the side of caution by having those forms at hand anyway.