Most people split the word in the wrong place.
English speakers tend to hear "heli-copter," and that habit has given us words like helipad and quadcopter. Wikipedia calls the split erroneous from an etymological point of view. The real break comes after "helico": the word is helico-pter, "spiral wing."
It comes from French hélicoptère, which Wikipedia says Gustave Ponton d'Amécourt coined in 1861. Etymonline also records the word in 1861. Wikipedia says it joins two Greek elements: helix, "spiral," and pteron, "wing." Britannica agrees on "spiral" and "wing." It states plainly that the word is not formed from "heli" and "copter."
The name described an idea more than a machine. Etymonline glosses the French term as a device for enabling airplanes to rise perpendicularly, more broadly a flying machine propelled by screws. The plan was to gain lift from spiral airfoils, and Etymonline notes bluntly that this approach did not work.
For decades the word stayed with experiments. Etymonline says it was applied to modern helicopters by 1918, once those began development. At that point a name coined for a failed design was handed to the aircraft that finally succeeded.
Other languages avoided the Greek. Etymonline notes that Flemish adapted the term as wentelwiek, "with rotary vanes."
The misreading did not stay a mistake for long. English speakers treated "-copter" as a suffix, and Etymonline records gyrocopter in 1915, formed from gyro- plus an ending modeled on helicopter. Helipad followed the same logic, and Etymonline dates the sense of a landing place for a helicopter or missile, "pad," to 1949.
The Greek helix is the source of English helix, a spiral, recorded in the 1560s. Etymonline relates it to a Greek verb meaning "to turn, twist, roll." So the machine is named for the thing its rotor does all day: turning.