Maybe. But Haiti broke loose very early on. They've been independent almost for as long as we have. Differences between English and French possessions might not have been as great then as they were later on.
The main difference AFAIK was that in Haiti the enslaved villages were moved from Africa whole, while in the British colonies in the new world the slaves were separated from each other as they were dispersed, so that the culture from the "old country" would have had less effect. To what extent the "maroons" of Jamaica were able to retrieve their African-based culture is a matter of ethnosociological debate, but it's fairly evident in Haiti, and to a lesser extent in Cuba.