“Carpenter” is from the Late Latin carpentum (“wagon, carriage, cart”), with a maker of wooden carts known as an artifex carpentarius. In English, “carpenter” replaced the word treowwyrhta, literally “tree-wright.”
“Carpenter” began to replace treowwyrhta in the 1300s, adopted from the Anglo-French carpenter (Old North French carpentier) and first specifically referring to someone who does heavy woodworking or makes items out of timber.
As I mentioned in the title, a Roman wagon- or cart-maker was known as an artifex carpentarius, with carpentum referring to any sort of two-wheeled wagon or carriage. In an unusual turn, though, Latin adopted this word from the Gaulish/Old Celtic carpentom, which is related to karros, or “chariot,” also the source of the English word “car.” The root of karros, then, is the PIE kers-, “to run,” which is also the source of the English words career, cargo, caricature, concurrent, currency and intercourse.
A semi-related tidbit: As you probably know, the profession of the Biblical figure Joseph is described in English translations as “carpenter,” a translation of the Greek noun tektōn (τέκτων), which was a general word for any artisan or craftsman. Tektōn is typically used to stand for the more general Hebrew noun kharash (חרש), “craftsman,” or the more specific kharash-‘etsim (חָרַשׁ עֵצִים), “craftsman of woods.” But some scholars speculate that the use of the term “carpenter/craftsman” in the Talmud may actually refer to someone wise and learned in a religious sense. The implication, then, is that Joseph (and Jesus) may not have been a literal carpenter, but someone of a more elevated social status (or, alternatively, another sort of craftsman).