1590s, "bewitch, enchant," from Middle French fasciner (14c.), from Latin fascinatus, past participle of fascinare "bewitch, enchant, fascinate," from fascinus "a charm, enchantment, spell, witchcraft," which is of uncertain origin. Earliest used of witches and of serpents, who were said to be able to cast a spell by a look that rendered one unable to move or resist. Sense of "delight, attract and hold the attention of" is first recorded 1815.
To fascinate is to bring under a spell, as by the power of the eye; to enchant and to charm are to bring under a spell by some more subtle and mysterious power. This difference in the literal affects also the figurative senses. [Century Dictionary]
Possibly from Greek baskanos "slander, envy, malice," later "witchcraft, sorcerery," with form influenced by Latin fari "speak" (see fame (n.)), but others say the resemblance of the Latin and Greek words is accidental. The Greek word might be from a Thracian equivalent of Greek phaskein "to say;" compare enchant, and German besprechen "to charm," from sprechen "to speak." Watkins suggests the Latin word is perhaps from PIE *bhasko- "band, bundle" via a connecting sense of "amulet in the form of a phallus" (compare Latin fascinum "human penis; artificial phallus; dildo"). Related: Fascinated; fascinating.
If [baskanos] and fascinum are indeed related, they would point to a meaning 'curse, spell' in a loanword from an unknown third language. [de Vaan]