He was ordained a priest on 5 August 1989 by Bishop Stanley Joseph Ott, for the diocese of Baton Rouge. Subsequently, he served in a variety of capacities within the diocese, including as pastor of the parishes of St. Joseph in Grosse Tete, Immaculate Heart of Mary in Maringouin and Sacred Heart of Jesus in Baton Rouge. He also served as parochial vicar of the parishes of St. George in Baton Rouge, St. Alphonsus Liguori in Greenwell Springs, St. Joseph Cathedral in Baton Rouge, and St. Isidore the Farmer in Baker. Fabre was elected to serve on the diocesan Clergy Personnel Board and served as chair of the Pastoral Planning Committee of the diocese. He at various times took on the roles of chaplain to St. Joseph's Academy, head of the diocesan Office of Black Catholics, Dean of the Northwest Deanery. He also served as a member of the College of Consultors, the Presbyteral Council, and the Diocesan School Board. He served as a Defender of the Bond within the Diocesan Tribunal.
On September 23, 2013, Pope Francis appointed Fabre as the new bishop to the Roman Catholic Diocese of Houma-Thibodaux in Louisiana. He was installed during a Mass at his Cathedral of St. Francis de Sales on October 30, 2013. As bishop of the Diocese of Houma-Thibodaux, he leads 125,000 registered Catholics, 39 churches and a number of chapels, missions, and communities.
On May 4, 2018, it was announced by Daniel Cardinal DiNardo, President of the United States Conference of Catholic Bishops, that Fabre would succeed Bishop George Murry, S.J. of the Diocese of Youngstown as the Chair of the Ad-Hoc Committee against racism. On November 6, 2018, Fabre released that addresses ongoing racism issues facing the United States and a Catholic's call to response. In the wake of the death of Mr. George Floyd in Powderhorn, Minneapolis, Michigan, Fabre along with Archbishop Nelson J. Pérez of Philadelphia, chairman of the Committee on Cultural Diversity in the Church; Archbishop Paul S. Coakley of Oklahoma City, chairman of the Committee on Domestic Justice and Human Development; Archbishop Joseph F. Naumann of Kansas City in Kansas, chairman of the Committee on Pro-Life Activities; Bishop Joseph C. Bambera of Scranton, chairman of the Committee for Ecumenical and Interreligious Affairs; Bishop David G. O’Connell, auxiliary bishop of Los Angeles, chairman of the Subcommittee on the Catholic Campaign for Human Development; and Bishop Joseph N. Perry, auxiliary bishop of Chicago, chairman of the Subcommittee on African American Affairs issued a The Statement had a special emphasis on the Solemnity of Pentecost and the call to "...pray and work toward a new outpouring of the Holy Spirit. Let us pray for a supernatural desire to rid ourselves of the harm that bias and prejudice cause. We call upon Catholics to pray to the Holy Spirit for the Spirit of Truth to touch the hearts of all in the United States and to come down upon our criminal justice and law enforcement systems. Finally, let each and every Catholic, regardless of their ethnicity, beg God to heal our deeply broken view of each other, as well as our deeply broken society."
