What language people speak in the West Indies has to do with who was the final winner in colonizing their land.
The same holds true on the American mainland. That is why people in the United States, a former British colony, speak English.
Spain was all alone at first in the game of colonizing America, but it did not stay lonely for long. By the seventeenth century, the English, French, and Dutch were all staking out American colonies of their own.
The West Indies, with their fertile soil, good harbors, and strategic closeness to the mainland, were a desirable property. Jamaica was captured by the English in 1655 and formally ceded to England in 1670. It is now an independent country.
Part of Hispaniola was ceded to France in 1697. That part is now the independent country of Haiti, where French is still spoken.