I was interested in a reference to Franz Bopp in Edward Said's Orientalism. In the libraries of Paris, Bopp had access to samples of ancient languages gathered by Napoleon's invasion of Egypt. It seems easier for linguists like Bopp to study change over time in their field, compared to Darwin sailing around the Galapagos gathering biological samples. Did the fields of comparative linguistics and natural science grow up together (like the von Humboldt brothers), or did theory from one influence the other first?
^(NB to any mods: I'm sorry if you saw a comment from me before — I hit save without realizing, and had to quickly delete it. )
The incredibly short answer is: yes! However, this isn't a very useful answer, not to mention an inappropriate one for the subreddit. I don't know much about Bopp and Edward Said, so I can't say anything on the specific example you gave, but I can talk more generally about the history of analysis of languages.
Historical comparative linguistics was, if not flourishing, then certainly extant well before theories of evolution were devised. Modern historical linguistics has without question been affected by theories of biological evolution, but I think I should also make clear a subtle point: languages do not evolve like species, and the overapplication of biological genetic theories to linguistic models is a real risk. Where large numbers of species are physically incapable of change through horizontal gene transfer without some intermediary agent, if two speech communities are placed into contact there is (arguably) no intrinsic barrier to language features spreading from one language to another, and vice versa. Uralic languages have borrowings from Indo-European languages; Middle English has phonological contrasts created by Norman French-English bilinguals; etc.
You raise a good question with regards to the development of natural sciences and linguistics: debates on the origin of languages certainly became much more widespread and vigorous in the 17th century and beyond, much as the practice of natural science grew and changed, however, I'm not confident I am qualified to give a causative relationship — is rationalism grounded in natural science first and foremost, or is it a more domain-general idea which motivated a change in how natural science was construed, just as it did linguistics?
Considering your other questions though, William Jones, an the early proponent of what eventually became the Indo-European language family, famously said this to the Bengal Asiatick Society [sic] in 1786:
“The Sanskrit language, whatever be its antiquity, is of a wonderful structure; more perfect than the Greek, more copious than the Latin, and more exquisitely refined than either, yet bearing to both of them a stronger affinity, both in the roots of verbs and in the forms of grammar, than could possibly have been produced by accident; so strong indeed, that no philologer could examine them all three, without believing them to have sprung from some common source, which, perhaps, no longer exists: there is a similar reason, though not quite so forcible, for supposing that both the Gothic and the Celtic, though blended with a very different idiom, had the same origin with the Sanskrit; and the old Persian might be added to the same family..." [emphasis mine]
In this, he proposes de facto an Indo-European language family with members of the modern Hellenic, Italic, Celtic, Germanic, and Indo-Iranian families featuring (the only major extant language family missing is Balto-Slavic, for some reason). His reasoning bears mentioning here — even without a preexisting theory to bias our intuition, no one can look at related languages and not notice the similarities; a number of others had proposed broad groupings of languages in the centuries before Jones, though they don't quite receive the same level of recognition.
This list of theorists does include a number of very familiar names, though: Dante imagined three distinct families of languages in Europe, "Northern"/Germanic, "Southern"/Romance, and "Eastern"/Greek+Slavic; while Leibniz figured there were two families in the region, "Northern" and "Southern" (Slavic languages were shortchanged once again), and noticed that Hebrew was related to Arabic, but not European languages like Latin and Greek. Between the two of them, Joseph Justus Scaliger, a French Calvinist from the second half of the 16th century, rejected a claim from before his time that Hebrew was the 'original' language from which all others spawned, and grouped European languages into four families based on the word for 'God' (Deus, Theos, Godt, Boge).
Though not exhaustive, I hope this does give you some sense of the historical linguistics background and the thoughts of scholars on the origin of languages in a pre-Darwinian era. I'm happy to try to elaborate on some things if you're interested.