As mentioned, I emailed the French side tourism office about who to contact if sick. I also asked about how quarantining would work. For example, where would one quarantine if staying in a hotel or AirBnB? I assume one option would be to just stay put, but I don't know for sure. That part of my email wasn't addressed. Here's what I got:

If feeling sick/contact: call emergency + 15 if symptons appear (cough,fever )

If test positive during your trip : the dutch authorities at the airport Juliana will advise you of the procedures.

Thank you sending your question to the following emails

CONTACT DETAILS

COLLECTIVE PREVENTION SERVICES – MINISTRY OF PUBLIC HEALTH, SOCIAL DEVELOPMENT AND LABOR
Email: ehas@sintmaartengov.org

SINT MAARTEN TOURISM BUREAU
Email: info@vacationstmaarten.com