The Punishment of Saint-Pierre by Alwyn Belinda gives the fullest account of the 1902 disaster and the decades of warning signs that preceded it — scientists, newspapers, and local officials who knew the volcano was threatening and chose not to act. It covers the political context (an election was days away, and the governor wanted voters to stay in the city) alongside the geology and the human stories of survivors.
Pelée of Martinique by Angelo Heilprin is an early scientific account of the eruption, written by a geologist who reached Saint-Pierre within weeks of the disaster. Published in 1903, it is out of copyright and available to read online. Heilprin's first-person description of walking through the ruins while they were still warm — ruins that are still visible today — is remarkable primary source material.
Strange Pilgrims by Gabriel García Márquez includes a story set partly in the Caribbean that captures the peculiar quality of disaster-haunted places. It is not about Saint-Pierre specifically, but travellers who have spent time in the ruins often find that García Márquez's feeling for history that won't leave is the closest thing to what Saint-Pierre feels like.
A History of Martinique by Sydney Daney is a nineteenth-century history of the island and has relatively little on the eruption (it predates it), but it provides excellent context for understanding what kind of city Saint-Pierre was at its height — the commercial capital of the French Antilles, more important than Fort-de-France, with an opera house, newspapers, and a population that considered itself the cultural heart of the Caribbean.