[3] He attended St. Anthony High School in Beaumont, where he was football team captain and senior class president.

[5] Fiorenza was named honorary prelate of his holiness by Pope Paul VI on December 5, 1973, and served as diocesan chancellor from 1973 to 1979.

[5] On September 4, 1979, Fiorenza was appointed the fourth bishop of the Diocese of San Angelo by Pope John Paul II.

On June 11, 2001, Fiorenza expressed his regret at the execution of Timothy McVeigh, a domestic terrorist convicted of killing 168 people in the Oklahoma City bombing in 1995.

The pope accepted his resignation on February 28, 2006, and appointed former coadjutor archbishop Daniel DiNardo as Fiorenza's successor.

[11] In a February 2020 lawsuit filed against the archdiocese, a man and a woman from Conroe, Texas accused Fiorenza of allowing the ordination of Manuel La Rosa-Lopez, despite a previous allegation of sexual abuse.

Fiorenza met with the girl's family at the time of the initial accusation and promised to remove La Rosa-Lopez from the parish and send him for treatment.