“Ballot” derives from French “balle”.

“Balle” has different meanings nowadays, all deriving from old Germanic word “ball”, the word for a small round object, itself from Indo-European root “behl” (blow).

Until the 17th century “balle” was used in French to name a bundle of goods, usually wrapped up in a piece of cloth. (Nowadays we’d translate “ballot” as “bundle” into English)
“Ballot” is a small “balle”, i.e. a small bundle one could carry on their backs and was first used in the 15th century.
The word “ballot” later gave another diminutive balluchon.

“Sac à dos” is a twentieth century word, the direct translation of German Rucksack and it is nothing else than a sophisticated “ballot” with two straps that go over the shoulders for easy carrying. The first “sacs à dos” were made of heavy cloth, they are the direct offsprings of the “ballots”.

My answer derives from various entries in Le Dictionnaire historique de la langue française (Alain Rey & al).