The Vareyn once lived in a fertile land at the head of a great desert, subsisting off of a great river and its bounty - until they were forced to leave after a catastrophic volcanic eruption.
Many years later, the Vareyn had long moved on to become a seafaring civilization, and after the ash had settled, a new people came to fill their place.
My question is, would these new settlers adopt parts of the Vareyn language?
Maybe. Probably not, but it really depends on how we fill in the gaps in your scenario. (FWIW, that's one reason why you're getting so many different answers.)
Newcomers to a land borrowing words (and expressions and phonetics and even grammatical features) from the language of the people previously living there happens all the time. Linguists even have a term for it: substrate influence. But normally that happens while the people speaking the old language are still there.
If the previous inhabitants are gone entirely, e.g. destroyed or driven far away by some catastrophe, then it's unlikely that just the inscriptions they left behind will have much effect on the newcomers' language, especially if most of the newcomers can't read them. Even if some of the newcomers do have the motivation and skill to decipher the old inscriptions (rather than just treating them as decorative art, or as evil heathen marks to be destroyed, as seems to have been common in real life), they'll probably just translate them into their own language. 121
Sure, you might end up with a handful of borrowed words for otherwise untranslatable technical or cultural terms, but probably not much more than that.
Things might be somewhat different if the two languages happened to share the same writing system, and if literacy was common enough among the newcomers, that most people finding the old inscriptions could actually read them. In that case you could perhaps get significant borrowing, especially if the two languages happened to be so closely related as to be at least somewhat mutually comprehensible.
On the other hand, if the new language was unrelated to the old one (but still sharing the same writing system), it seems more plausible that the old inscriptions would just seem like gibberish to the newcomers. Now, a common human reaction to seeing something unreadable but clearly meaningful carved in stone seems to be "It must be magic!" So a plausible outcome of this particular scenario could be a bunch of words from the old language being adopted into the new one, but with completely different meanings, as people claiming (falsely) to be able to understand the old language would pick more or less random phrases from it and use them as "barbarous names", inventing new mystical meanings for them.
But of course, none of those scenarios really match yours in one respect: your Vareyn people are still alive, although living in completely different region and with a different lifestyle. That, in turn, raises a bunch of questions:
* Did any Vareyn remain in the old lands, or return there after the catastrophe? If not, why not? (It's rare for people to entirely abandon a land, as long as as it's even marginally livable and as long as they're not forced out of it by other people moving in.)
* If all the Vareyn left, did they move far away, or did they stay close enough that the new people settling their old lands would know of them? (And, if the latter, why didn't the Vareyn themselves resettle the old lands once it was possible again?)
* How much of their old culture and language do the new "sea Vareyn" retain? Can even they read the old inscriptions, or understand the old Vareyn language? Do they even know where their old homeland was?
If some descendants of the old Vareyn did stay in or near the old lands, or return there once the worst of the catastrophe was over, that could provide the kind of linguistic continuity needed for a proper linguistic substratum. It doesn't really matter if there are only a few of them — all that's needed is that they're there, and they they can read the old texts in their own language and teach that language to the newcomers.
On the other hand, if the Vareyn moved far away from their old homeland, it's possible that the newcomers might not even know that the Vareyn still exist somewhere. In which case it doesn't really matter whether they do or not, as far as the newcomers are concerned.
Indeed, if enough time has passed, even the Vareyn themselves might have forgotten exactly where their old homeland was, and their culture and language could easily have changed beyond recognition. They might not even be able to read the old Vareyn inscriptions themselves, e.g. 111