Is this a run-on sentence?
A helium-filled balloon called the Double Eagle II completed the first transatlantic balloon flight in history in 1978, it landed in a barley field near Paris about 140 hours after lifting off from Presque Isle, Maine.

 - no
 - yes
This is a run-on sentence. It is a comma splice formed from two sentences run together, joined by just a comma.
A helium-filled balloon called the Double Eagle II completed the first transatlantic balloon flight in history in 1978, it landed in a barley field near Paris about 140 hours after lifting off from Presque Isle, Maine.
Here is one way to fix the run-on sentence:
A helium-filled balloon called the Double Eagle II completed the first transatlantic balloon flight in history in 1978. It landed in a barley field near Paris about 140 hours after lifting off from Presque Isle, Maine.