c. 1200, "incapable of producing its kind" (of female animals, plants), from Old French baraigne, baraing "sterile, barren" (12c.), perhaps originally brahain, a word of obscure derivation, possibly from a Germanic language. Its use in reference to males is rare. Of land, "producing little or no vegetation," by late 14c.
As a noun from mid-13c., "a barren woman;" later "tract of more or less unproductive land."
BARRENS. Elevated lands, or plains upon which grow small trees, but never timber. [Bartlett, "Dictionary of Americanisms," 1848]
word-forming element denoting action, quality, or state, attached to an adjective or past participle to form an abstract noun, from Old English -nes(s), from Proto-Germanic *in-assu- (cognates: Old Saxon -nissi, Middle Dutch -nisse, Dutch -nis, Old High German -nissa, German -nis, Gothic -inassus), from *-in-, originally belonging to the noun stem, + *-assu-, abstract noun suffix, probably from the same root as Latin -tudo (see -tude).
<a href="https://www.etymonline.com/word/barrenness">Etymology of barrenness by etymonline</a>
Harper, D. (n.d.). Etymology of barrenness. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/barrenness