Just a minor correction: the TV service for France's overseas territories is now known as Outre-mer La Première after a reorganization of French broadcasting several years ago. It uses the La Première brand on the air.
The French part of St. Martin was administratively a part of Guadeloupe until 2007 and is officially served by the La Première station on that island. For instance, Guadelpoipe La Première has a St. Martin section on its website:
Retrouvez toute l'actualité 'Saint-Martin' et les dernières informations en direct, les articles et analyses, regardez les vidéos et les photos et bien plus encore avec Guadeloupe La 1ère.
la1ere.franceinfo.fr
It also airs reports from St. Martin (I don't know how frequently) and, from what I've seen on YouTube, produces election specials for that island.
You would known better than I would how widely Guadeloupe La Première is distributed on St. Martin given the predominance of English on the island.
Here's a typical La Première newscast for Guadeloupe; I didn't catch any St. Martin stories in this edition:
Guadeloupe is also served by a commercial service, Canal 10, but don't know if that station makes any effort to serve St. Martin.