The word has Jew in it, and my understanding is that Jews were often pushed into things like making jewelry or banking by many European societies. How correct (if at all) is this assumption? And are there any actual connections between the word and the stereotype? (Interestingly enough, the word cliche actually comes from the french verb clicher, meaning to stereotype.)
No, the etymologies are entirely unrelated.
From the OED:
Etymology: < Anglo-Norman juel, jeual, = Old French joel (nominative singular and object plural joeaus, joiaus), 12th cent. in Hatzfeld & Darmesteter, 13–14th cent. jouel. 14– 15th cent. joiel. joiau, modern French joyau: compare Provençal joell, joyel, Catalan joyell, Spanish joyel, Italian gioiello; all apparently < French.
The etymology of the French word is still a matter of dispute; some see in it a derivative of Latin gaudium (quasi *gaudiellum ), whence French joie , joy; others of Latin jocāre , whence French jouer to play, or of the cognate jocus , French jeu play, through a derivative jocāle . Compare also juelet n. The medieval Latin was (13th cent.) jocāle, plural jocālia. See Diez, Littré, Schéler, Hatzfeld & Darmesteter, Körting Lat. Rom. Wbch. s.v. jocālis.
no. it's from a french word that sounds similar.