I understand how the governors and urban merchants and their descendants would switch to Latin and its descendants.
What I don’t understand is how the peasants switched languages. How did that happen?
While more can be said or asked about it, you might find some elements of answers in these previous posts.
Would a 2st Century farmer in Roman Gaul speak Latin at home, or Gaulish?
Why is it that places like Gaul/France and Spain/Hispania eventually adopted a form of Latin as their language?](https://www.reddit.com/r/AskHistorians/comments/p9w945/comment/ha15ui2/?context=3)