North Africa starting from Tunisia and going west was firmly part of the Western Roman Empire for the better part of several centuries. Gaul, Iberia, and even modern Romania were almost completely Latinized by the time Rome fell. Was North Africa similar, or were the Berber languages more widespread?
Northwest Africa is a fascinating case, let me bring up my notes from the Independent Study I did on Roman Africa (mostly based on the book Rome in Africa by Susan Raven). Roman Africa took a different path from the rest of the empire in many ways, due to it being a meeting place of Greek, Phoenician/Punic, Roman, and African influences.
It's hard to say exactly how Latinized the local population was, since most of the writing we have was written by elites. But to make an educated guess, we have to go a little further back in history.
Before Rome conquered Northwest Africa, the Greeks and the Phoenicians colonized the region, but they mostly settled in coastal areas and the pastoral Berbers occupied more inland areas. When the Romans conquered Carthage, they wanted to exploit the agricultural potential of the region (in ancient times North Africa was lush and fertile), so they began to push the ethnic Berber population south to make room for farms. This southward expansion continued for centuries, with Rome gobbling up the land and pushing the Berbers practically into the desert, only allowing them into Roman territory at certain times of year to help with the harvest. So the Berbers retained their language, but lost most of their land.
The farms were mostly settled by Romans, many of them military veterans, who certainly spoke Latin. The ethnically Punic (Carthaginian) residents of the conquered cities probably began speaking Latin, because Punic is known to us pretty much only through early inscriptions and Latin translations, indicating that the Punic language declined with the rise of Roman influence.
When the Germanic Vandals conquered Northwest Africa in the 430s CE, they began speaking and writing in Latin, indicating that this was the dominant language in the region at that time. However, with the decline of the Vandal interregnum, Berber kingdoms sprang up and started nibbling at the Vandal borders, indicating that the Berber language and culture were never fully extinguished.
So, what we have is a linguistically diverse region where Latin certainly played a dominant role, being the language of choice in Roman and Vandal territory, but never fully displaced local African languages among Berber populations.
Hi there! I actually asked a similar question a few months back, and there was a pretty good answer that might give you some of the picture, but we could still certainly use responses that are more relevant to NW Africa and closer in time to the 7th century.