Monsignor Teurlings was succeeded by a Canadian priest, Father Charles B. Fortier. He built Teurlings Catholic High School at its present location on Teurlings Drive. He also replaced the first rectory with the rectory that stands today. Father Fortier was succeeded by Monsignor Rudolph Arlanti, a native of Italy and the former chancellor of the Diocese of Lafayette. He gave firm support to the parish activities and to its two schools. The successor of Monsignor Arlanti, Monsignor Alexander O. Sigur, was the first native-born priest to serve as pastor of St. Genevieve's. However, he was soon called to be rector of Notre Dame Seminary in New Orleans. He was replaced by another native of the Diocese, Monsignor Charles Marin. Bishop Jules Jeanmard was succeeded by Bishop Maurice Schexnayder. Bishop Schexnayder was a strong supporter of Catholic schools and a frequent visitor to St. Genevieve's. After his retirement, Bishop Gerard L. Frey was appointed the third Bishop of Lafayette and took office on January 7, 1973.
Bishop Frey appointed Monsignor Marin, pastor of St. Genevieve’s, as the Vicar for Clergy. The Bishop's brother, Reverend Jerome Frey of the Society of Mary, became the sixth pastor of St. Genevieve’s. He was the first religious priest to assume these duties. He was joined in his ministry by two co-pastors, Father William B. Havenar and Father Rex Broussard. This ministerial team was succeeded by the seventh pastor, Reverend Floyd J. Calais, on February 4, 1977. In 1982 Fr. Joseph F. Brennan took the reigns of the parish for over fourteen years. During this time the Missionaries of Charity joined the parish in service to the less fortunate in the bayou area (Seafood Lane) of the parish where a chapel was established. His pastorate also saw the paving of the church parking lot and the erection of Mystical Rose Hall to replace the now deteriorated Pavilion. In 1996 Fr. Jody Simoneaux succeeded him and undertook a renovation and expansion to the Teurlings High School Campus and the building of the new St. Geneveive Middle School complex. On July 2, 2007 after three years of canon law studies in Rome, Fr. W. Curtis Mallet, JCL, became the tenth and current pastor of St. Genevieve Pastor.
In addition to the pastors who shepherded St. Genevieve, many other priests have served. They served the spiritual needs of the parishioners by strengthening and comforting, teaching and preaching, visiting the sick, burying the deceased, and supervising the many organizations and the general operation of the parish.
Associate Pastors included Frs. Gene Lafleur, Bede Becnel, Leslie Prescott, Guy Lemoine, John Windt, Msgr. Robert Landry, Frs. Fred Swenson, Conley Bertrand, Carey Landry, Robie Robichaux, Steven C. Leblanc, Roger Moag, Louis J. Richard, Allen Breaux, Daniel Picard, Willard Dugas, Thomas Voorhies, Bill Melancon, W. Curtis Mallet, Aaron Melancon, Mitchell Guidry, Mikel Polson, Richard Broussard, James Nguyen, Kenneth Broussard, Kevin Bordelon, and Blair Lope M. Sabaricos. There were many others who, as visitors, deacons, or seminarians, also aided the pastors in their responsibilities.
Priests are not alone in building up the Church for Christ in parishes. There were and are countless numbers of parishioners who have generously given of their time and talents. They have done everything from gardening and sweeping to taking census, teaching catechism, fund raising, housekeeping, secretarial work, bookkeeping, and answering telephones. In a thousand ways, they have promoted the good of the parish and helped to provide for the needs of others. Many have gone to their reward, and their good works are now known only to the Lord. Others have been forced to retire from an active role, but they still retain a deep love for St. Genevieve’s. None of them will ever be forgotten, for their good works have become the inheritance of the present parishioners. A special debt of thanks is due to the many nuns who labored patiently in the parish schools to bring Christ in a special way to the children of the parish. The many lay teachers who collaborated with these nuns are also gratefully remembered. This is to say nothing of the many people who today belong to the parish organizations and participate in the sacred liturgies in song, word, or other special ministries.