The statement is - False.
Quebec, after World War II, and still in the present, has largely remained a place with homogeneous culture. Around 85% of the population is francophone, thus the French culture is dominating by far to any other culture. Despite having around 15% of the population that do see the French culture as their primary culture, considering the fact that in those 15% there's around 60 ethnic groups, with very small numbers, the picture is clear. Even the English culture hasn't been able to mix up the things and make the Quebec culture more diverse, while the other cultures deriving from Europe, Asia, or Africa, are usually assimilating with the local one within a generation or two.