You don't need to be of strong faith to enjoy the serene atmosphere of Balata Cathedral. Look up when the next mass starts or when you can go for a wander through.
When you've finished up at this principal church in Fort-de-France, why not make your way to Pointe du Bout Beach, Anse Mitan, and Marina of L'Etang Z'Abricots? They're near Balata Cathedral and also a hit with many travelers.