OED gives the following origin for candy:
French candi in sucre candi ; compare Italian zucchero candi (found, according to Littré, in an Italian author of 1310), Spanish azucar cande , Portuguese assúcar candi , medieval Latin saccharum candi ;
< Arabic, originally Persian qand sugar, the crystallized juice of the *sugar-cane* (whence Arabic qandah candy, qandī candied); of Indian origin, compare Sanskrit khanda ‘piece’, also ‘sugar in crystalline pieces’, < khand to break.
The mention of sugar-cane made me wonder whether it had the same Semitic roots as cane.
Middle English canne, cane, < Old French cane, later canne (= Provençal cana, Spanish caña, Italian canna) < Latin canna, < Greek κάννα, κάννη, reed, perhaps < Semitic: compare Hebrew qāneh, Arabic reed, cane.
So ... maybe? Wiktionary traces both words to the same Sumerian roots, but those pages don’t have external references.