Betas for over 100 canyons here: http://ankanionla-madinina.com/Martinique/Martinique%20inventaire.htm - Coordinates are UTM, zone 20P.
Martinique has a LOT of explored canyons. Most are well maintained, with excellent anchors and approach and exit trails. In general, things are more straightforward than canyoneering in the US, but less so than in Europe. There just aren't many canyoneers on Martinique.
There is a canyoning club that runs trips for members 1-2 times a month, and offers classes. As of 2022, this is maybe two dozen members. The club, Ankanionla-madinina, is accessible and open. There are usually a few members who speak some English if you don't speak French. Otherwise, canyons are free and open, and no permissions are needed.
Be advised, despite the high number of routes, many are not very good. However, there are several world-class routes hidden in the vast beta. Choose carefully if you visit on a short trip.
More information at: http://www.lukaseddy.com/canyons-of-martinique/