It could be old Basque (ie. pre 14th-century)

People chatting in Old Basque? So this is scripted? Seems unlikely.

PS: Yes, Old Basque is a language...

No, that's a misleading description. All languages are literally prehistoric, coming from ancient times (prehistory). English comes from Old English, from Proto-Germanic, from Proto-Indo-European, etc. When people say "Basque [etc.] is an old language" they invariably mean something other than age. That's like me telling you that my ancestors are older than your ancestors. I know this seems like an unimportant point, but this leads to very slippery (often meaningless) arguments and claims about languages like Basque.

Basque has been in [western] Europe probably* longer than any other language, but that's distinct from it being "old", and that's important to emphasize.
[*There's no direct evidence of this. Actually other languages are attested earlier, but there's no reason to believe Basque spontaneously appeared sometime after the earliest records of other languages.]

For more about Old Basque...

I only skimmed what you wrote so I can't address the details, but you really should look into Acquitanian. It's untrue that we know nothing of the history of Basque, nor that Basque is entirely "isolated". It's just hard to link it up to other familiar or modern languages.