Of course Jesus was free from original sin, but did he have concupiscence to deal with?
Jesus did not have concupiscence because he was free from original sin (this also means that Mary was free from concupiscence as well). As the Catechism of the Catholic Church (2515) puts it:
Concupiscence stems from the disobedience of the first sin. It unsettles man’s moral faculties and, without being in itself an offense, inclines man to commit sins (emphasis added).