word-forming element meaning "not, opposite of, without" (also im-, il-, ir- by assimilation of -n- with following consonant, a tendency which began in later Latin), from Latin in- "not," cognate with Greek an-, Old English un-, all from PIE root *ne- "not."
In Old French and Middle English often en-, but most of these forms have not survived in Modern English, and the few that do (enemy, for instance) no longer are felt as negative. The rule of thumb in English has been to use in- with obviously Latin elements, un- with native or nativized ones.
"alleviate the grief or mental distress of," 1690s, from French consoler "to comfort, console," from Latin consolari "offer solace, encourage, comfort, cheer," from assimilated form of com-, here perhaps an intensive prefix (see com-), + solari "to comfort" (see solace (n.)). Or perhaps a back-formation from consolation. The Latin word is glossed in Old English by frefran. Related: Consoled; consoling.
<a href="https://www.etymonline.com/word/inconsolable">Etymology of inconsolable by etymonline</a>
Harper, D. (n.d.). Etymology of inconsolable. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/inconsolable