It's extremely rare and, as far as I know, limited to people who are coming back from territories outside the EU where a “variant of concern” is circulating but it does exist. In that case, you do get a paper (an arrêté préfectoral naming you specifically).
If you are vaccinated and test positive while you are in France, isolation is recommended but that's quite different from a compulsory quarantine. Obviously, you shouldn't board a plane or a train (and could in fact be denied boarding if a negative test is mandatory, e.g. going to Italy) but I don't see your insurance covering that event, given the language you quoted.
When you get a test in France, it will be entered in the SI-DEP and you get a link to download a certificate of the test results even if you are not covered by the French health insurance system. I assume this is also the case if the test comes back positive (and I have always been assured I would get a call from the lab/pharmacy in that case). You should also receive “advice on what you have to do”. Realistically, case numbers are so high that in all likelihood nothing else will happen after that.