Having sung and heard "O Holy Night" thousands of times in my life, it's a little surprising that only recently did the phrase "His law is love and His gospel is peace" really catch my attention. The angels who were sent to announce the arrival of the Saviour in human baby form declared, "Glory to God in the highest, and on earth peace, goodwill toward men." That's the New King James. The English Standard version says,"...on earth peace among those with whom he is pleased."
Have you ever noticed that pretty much every time an angel appeared to somebody, they were afraid? When an angel appeared to Zacharias in Luke 1, "he was troubled, and fear fell upon him." When the angel appeared to the shepherds in Luke 2, "they were greatly afraid." But when the angel Gabriel came to Mary in Luke 2, her reaction was different. There is no mention of fear, but it was his greeting that troubled her. He said, "Rejoice, highly favored one, the Lord is with you; blessed are you among women." Having grown up under the Law, she doubtless considered herself, as our natural selves tend to do, as not "highly favored" and not "blessed" but rather as falling far short of the mark of what God required.
It is so natural for us to default to the condemnation, "God can't possibly be pleased with me" mode. However, there is an amazing line in Jesus' solitary prayer to His Father just before His arrest. In John 17:23, He is praying for unity amongst His followers, "so that the world may know that You sent Me, and LOVED THEM AS YOU HAVE LOVED ME." Our God and Father loves us just the same way He loves Jesus. And our present state is that we HAVE peace with God (Romans 5:1). His law IS love, and His gospel IS peace!