It might be easiest to see this in the case of Passover. We actually repeat a refrain directed to how this feast has been fulfilled in Christ. Christ, our Passover lamb, has been sacrificed. Let us therefore celebrate the festival with the unleavened bread of sincerity and truth. Christ is not only the Lamb sacrificed but the priest sacrificing, the host and victim. It is not that Christ is in the Seder but He IS the Seder and this we acknowledge and celebrate every Sunday ( a mini Resurrection Day).
But the connection most of us ought to make is Pentecost. The readings for Pentecost remind us that this was not a Christian Day but the fulfillment of the prophet Joel and the words of Christ. Pentecost, also called the Feast of Weeks, Harvest or Shavuot, is a harvest festival and a remembrance of the Lord giving the Torah to His people. Christ is then the harvest, the fruit of the promise given from Eden and planted in the hearts of His people by faith and Christ is not only the giver of the Law written by the Spirit into our hearts but the fulfillment of the Law for us. All of this combines as the Church is sent forth into the harvest fields readied by the Spirit so that the Lord might bring forth a rich harvest of souls.
St. Paul connects Day of Atonement to our Lord and Good Friday is that day when the promise of a sacrificial lamb is fulfilled in the Lamb of God who takes away the sins of the world. All of this is again manifest on Sunday morning when we sing to Christ the Lamb as the host is elevated for our acknowledgement of faith and adoration. The Temple veil is rent from top to bottom and the function of the Temple, always to point to Christ, is fulfilled and the building is soon destroyed. Christ is our Temple, the Lamb of sacrifice, where the Atonement is made and we are set free to abide in Him both now and forevermore. This, too, is the central focus of the Sunday liturgy as the faithful sing to Christ and receive His flesh and blood in the sacred mystery of this communion.
Therefore let no one judge you by what you eat or drink, or with regard to a feast, a New Moon, or a Sabbath. These are a shadow of the things to come, but the body that casts it belongs to Christ. (Col 2:16-17). Check out also Romans 14.
So it is not true that the Christian calendar ignores or replaces the Jewish calendar. The reality is that we are not play acting, not re-enacting, but observing the ancient feasts in the way God has appointed by honoring Him who fulfills them. This is the way that they are being observed forever and in this way the feasts are not simply for the few but for the many as Gentiles take their place within the promise without first being circumcised and becoming Jewish. All of this should enrich our celebration of Easter as the season in which all of these things are fulfilled in Christ -- for they pointed to Him!