We went to Anguilla and they checked the passport in Marigot before leaving SXM. I asked what exactly are you checking and they said they are checking to see if the passport is valid for at least 6 months. So keep that in mind if you leave SXM for a day trip.
You can go to AXA and return to SXM via the Dutch side. We did a day trip last month and never left the Dutch side. Not sure how this would work as I don't know if it is a French St. Martin requirement or an AXA requirement but there are options instead of going via Marigot.