Kutscher writes that names for metals have a tendency to "wander" from land to land, and therefore it is difficult to place their origin. I found this quote discussing barzel (I recommend reviewing the entire thread):
There is an article by G. Rendsburg in Scripta Mediterranea 3 (1982), pp.54-71 (Toronto):
Semitic przl/brzl/brdl, "Iron"* Rendsburg starts off stating that the etymology is most obscure. He eventually proposes an original *br, borrowed from some non-semitic proto-language, meaning copper or metals in general, from which came *brz which he took to be an early word for iron. The addition of -l to make brzl came later in Canaanite, Akkadian and Ugaritic which were probably borrowing from each other (p.55; fig.1, p.58). Rendsburg also links *brz with Indo-European bronze/brass.
Stahl writes that barzel derives from ברז, meaning "to drill, bore". In Aramaic we have the word birza ברזא - a hole in a barrel, which became the source of the modern Hebrew word for spout, faucet - ברז berez.
(Berez also gives us the Hebrew slang phrase: דפק לו ברז / שם לו ברז dafak lo berez / sam lo berez, which means "to not show up", and the verb להבריז - "to ditch (abandon)". Almagor writes here that there is disagreement as to why a berez is an obstacle: some say the closed berez prevents the water from running, others say the water from an open berez causes the problem. However, Rosenthal writes that in North African Arabic, birez means "to slip out of one's hand".)
To return to barzel, Klein writes of the etymology:
A loan word from Hittite barzillu, whence also Akkadian parzillu, Moab. and Phoen.ברזל, Ugar. brsel, Aram. and BAram parzel פרזל ( = iron). Arabic firzil is an Aramaic loan word. Latin ferrum (= iron) is a Semitic loan word. According to my opinion the loss of the Semitic ending -el, resp. -illu, is probably due to its having been mistaken for the Latin dimin. suffix -ellus, -illus, and consequently dropped.
Kutscher agrees that the word barzel does not seem and sound Semitic in nature. As far as the connection to the Latin ferrum (the source of the symbol Fe for the element iron), he provides an interesting piece of evidence. There is an ancient iron mine in Italy, on the "route of the iron", called Fursil (near the Castle of Andraz) whose name is remarkably close to parzel. Perhaps this place preserves the original Latin form of the word.