I have been reading that the term Romanization is starting to fall out of favor among historians and archeologists, so perhaps I should rephrase the question. In other words, how quickly did it take for citizens of Gaul to start to incorporate Roman culture into their everyday life? Why were the Romans so successful in spreading their culture across Gaul?
I wrote a bit about the problem of Romanization and the way such things might play out in response to this question yesterday, you might find it interesting (the tl;dr version of it is, essentially, that Romanization was so successful because it didn't try to romanize people). I won't try to comment on the situation in Gaul since I'm really only familiar with the two Germanias and Pannonia Superior in that regard, and there are others here who can probably do a lot better. The book by Woolf would be my go-to resource to recommend to the interested.