Do Catholics believe that Jesus was a Jew?
Yes, of course. From the Catechism of the Catholic Church:
We believe and confess that Jesus of Nazareth, *born a Jew of a daughter of Israel *at Bethlehem at the time of King Herod the Great and the emperor Caesar Augustus, a carpenter by trade, who died crucified in Jerusalem under the procurator Pontius Pilate during the reign of the emperor Tiberius, is the eternal Son of God made man. He “came from God,” “descended from heaven,” and “came in the flesh.” For “the Word became flesh and dwelt among us, full of grace and truth; we have beheld his glory, glory as of the only Son from the Father. … And from his fullness have we all received, grace upon grace” (CCC 423, emphasis added).