Pretty simple: is there the same word in Latin ?

• Yes ? -> It’s borrowed from Latin.

• No ? -> It’s not.

If it’s not borrowed from Latin it can still have a Latin etymology (like in “empereur”, which is not a latin word)

I don’t think the “middle ground” words are that different from inherited words. Just because they went through less change doesn’t mean they were imported later, or that they are “less inherited and more borrowed”.

Apart from that, it’s fairly easy to know if a word is borrowed or inherited. Is it originally a scientific word ? Biology, psychology, mathematics ? If so, it’s borrowed. It can also extend to literature or philosophy.

Anus is a medical term. Like fémur, tibia, it’s directly Latin.

Cactus is Botany vocabulary. We didn’t have another word than the Latin one so we used it.

If you have other example that don’t fit in this tell me, I’ll try to expand the “rule”, but it should cover most of it.

The criterion is continuity. In the course of the historical development from Latin to modern French, was the word always present? Then it is considered inherited.

Was it at some point not present, then introduced from a language that was, at the time, not the same language as (whatever phase) French (was in)? Then there was discontinuity, and the word is considered to have been borrowed at that time from that other language.

A word can be the result of the direct evolution of a preexisting word in the same language as its pronunciation and spelling rule evolves too or can be picked as is or adapted from a foreign language at some time.

The first kind is what you describe as inherited, the second form is what you describe as borrowed.

Things are of course not always that simple.

Chat used to be felis in classical Latin, and only became cattus later, probably from an African or Middle East origin (Kadis in Nubia or Gato in Syria), so it is "inherited from borrowed".

Some words like empereur are clearly of the first type (with emperere as intermediary step) while impératrice belongs to a third class: it is a word that has been restored to a spelling closer to its Latin roots by scholars, as in old French, empereriz and variants like emperreriz, empereresse, emperesresce, empeerris, empeirreis, emperix, emperies, empereys, emperice, amperice, emperresse, emperesse, empereise, anperaice, eporaice were used.

I mean, the main criteria are the sound changes from Latin to French. (This is a little circular, since examining the native vocabulary is also how we deduce these sound changes, but it’s not fallaciously circular). A word like “feu” < Latin focus shows characteristic French sound changes such as the loss of unstressed vowels, the vocalization and ultimate loss of intervocalic single /k/, and the change of “o” to “eu”.