*nek- (1)

mid-14c., "doing no evil; free from sin, guilt, or moral wrong," from Old French inocent "harmless; not guilty; pure" (12c.), from Latin innocentem (nominative innocens) "not guilty, blameless; harmless; disinterested," from in- "not" (see in- (1)) + nocentem (nominative nocens), present participle of nocere "to harm," from *nok-s-, suffixed form of PIE root *nek- (1) "death."

Meaning "free from guilt of a specific crime or charge" is from late 14c., as is the meaning "with childlike simplicity or artlessness." Humorous sense "free, devoid of" is from 1706. The noun meaning "person who is innocent of sin or evil, artless or simple person" is from c. 1200, especially a young child (who presumably has not yet sinned actively). The Holy Innocents (early 14c.) were the young children slain by Herod after the birth of Jesus (Matthew ii.16), hence Innocents day (Dec. 28).

Indo-European words for "innocent" are generally negative compound of the word for "guilty." An exception is the Germanic group represented by Gothic swikns (also "pure, chaste"), Old Norse sykn "free from guilt, innocent" (especially as a law term), Old English swicn "clearance from a charge," also "cleansing," but these are of uncertain origin.

"harmless, producing no ill effect, incapable of harm or mischief," 

1590s, from Latin innocuus "harmless; innocent; inoffensive," from in- "not" (see in- (1)) + nocuus "hurtful," from root of nocere "to injure, harm," from *nok-s-, suffixed form of PIE root *nek- (1) "death." Related: Innocuously; innocuousness.