We do know that Celtic speakers quickly adopted latin as their language at a very rapid pace but often merged it with their Celtic languages. The Romans loved to complain about the Celts butchering Latin. There are comments about those very people in Iberia / the pyrenees speaking far better Latin than the Celtic speakers. This is likely because they didnt really merge in their language due to them being very different languages not even of the same family. It's thought the reason French sounds the way it does is because of the large Gaulish influence. The Celto-Italic language only diverged into the various Celtic and Itallic languages well short of 1,000 years prior to the Roman conquest of Celtic lands. The Celtic expansion across Europe just prior to Roman expansion worked out really well for the Romans.The Iberian language has nothing to do with Latin and Celtic languages, it's speculated to be related to Basque, and they all adoted Latin. Same as with North African languages (Afroromance was an extinct language but it existed). They reason has nothing to do with language similarity but with the elites speaking Latin.
Anyway, Iberia was over half Celtic speaking at this stage, as Celts had been spreading into iberia, and there was a lot of mixing between them and the other iberians, it gets quite messy. Iberia is quite fascinating, because it was quite celtic dominated, with a decent helping of other languages which we aren't quite sure what they were related to, then it had a few Greek cities on the coast and a bunch of Carthaginian cities, and just prior to Roman conquest all of the non-celtic areas were entirely under Carthaginian rule. So they became a very linguistically mixed area which was very Celtic heavy at the time of Roman rule, which aided in the linguistic shift as Latin could be used as the lingua franca and was easily adopted by the Celtic speakers.
As for North Africa, I'm not actually sure how much of North Africa spoke Latin. From what I have been able to find it seems to have mostly been spoken in the Roman cities, and was not the dominant language. Punic continued to be spoken in the area, and the Numidian language(s) were quite dominant as well. It wasn't homogenised into some purely Latin speaking group at all.
At any rate, look up a map of the Celtic expansion across Europe, it's an extensive stretch of territory. This expansion very much paved the way for Roman expansion as not only did it make it easier for them to Romanise the areas, but the Celts were not this barbaric tribal people they are often portrayed as, but they tended to build cities and roads, with trade and crafts etc. So there was an existing structure there which Rome could subsume and build their system on top of. This facilitated that gradual Romanisation.
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