The Taíno, the original inhabitants of the island, were wiped out / assimilated by the Europeans who settled the island. Years later the Spanish and criollo settlers relocated to the east of the island leaving the west free for the French to develop.
The French and the Spanish had different cultures and radically different strategies on how to develop their colonies and thus the island ended up with two different cultures and governments and languages and political systems and with people of different (but overlapping) racial composition.
A lot of people wrongly assume that Caribbean is an ethnic group but that couldn't be farther from the truth. I'm a Puerto Rican and I have a lot in common with Dominicans and Cubans because the three territories are former Spanish colonies. But I have little in common with Haitians, Jamaicans or the inhabitants of the smaller islands of the archipelago. To illustrate my point, I have an archipelago 40 miles east of where I live and we have no ferry between the islands and no connection of any sort beyond the fact that we're both US territories. I've been there as a tourist but nothing more.