The sentence is grammatically correct, but it is hard to parse.
At first, I thought "the Haitian mulatto" was the complement of "on". I needed to read the rest of the sentence to be able to understand that "on" was an adverb.
My first recommendation is to add a comma:
From the colonial period on, the Haitian mulatto and black bourgeoisie have embraced the Catholic religion, European culture, French language, and Western ways.
I also recommend using "onward" instead of "on" for clarity. This is because "on" is also a preposition, which was the source of my confusion. Whereas "onward" is unambiguously an adverb:
From the colonial period onward, the Haitian mulatto and black bourgeoisie have embraced the Catholic religion, European culture, French language, and Western ways.
Depending on the context of the sentence, you might want to simplify it even more:
Since colonial period, the Haitian mulatto and black bourgeoisie have embraced the Catholic religion, European culture, French language, and Western ways.