Lucie--the biggest problem with October 1 week is that it is hurricane season. That said, I often travel to St. Maarten/St. Martin in hurricane season and did so in October 2021. The weather at that time of year is warmer than most of the rest of the year, and not really significantly more rain than other times, UNLESS of course you happen upon a hurricane or a tropical storm. If you do decide to travel that time of year, just make sure you buy travel insurance. Usually the island is pretty quiet at that time of year, which I consider to be a good thing.
Curious, as to why you say you only have availability that week. Is that your personal schedule, or are you trying to book a timeshare or something?
And you said "St. Martin". Are you specifically looking at travelling to the French side, as "St. Martin" is the official name for the French side of the island only. If you are interested in the French side in particular, a lot of restaurants on the French side often close for vacation during that time period.