For staying on the French side I would assume you could follow the rule for flying into the Grand Case airport :

(Vaccinated people aged 12 and over traveling to/from France to/from Grand Case:
Must provide proof of honor that they are symptom-free and unaware of having been in contact with a confirmed case of covid-19 in the fourteen days prior to the flight.)

Just read the post about the French requirements. Never new that unvaccinated were not allowed to go to St Martin without isolating for 7 days, assuming I am reading it correctly. So I guess Americans will still need to get a test to stay on French side.