I am thinking of visiting a french territory in the carribean-which place is a must see & why?

I don't believe in 'must see' places. Study them all and decide for yourself.
Strictly speaking, France has no territories in the Caribbean.
There are islands considered part of the mainland (not sure how that works) and 'collectivities' (not sure how they work either).
Gaudeloupe, St. Martin, Reunion, Martinique, St. Barthelemy, and Mayotte are the ones I know about. I have been to St. Martin, but it was 35 years ago. Not really part of the Caribbean. The Antilles.