D. Francisco I de Saldanha da Gama (May 20, 1723 – November 1, 1776) was the third cardinal patriarch of Lisbon (from 1758).
He studied canon law at Coimbra and was appointed a cardinal by Pope Benedict XIV in 1756, and named Patriarch of Lisbon on July 25, 1758. He was the great-grandson of Margarida de Vilhena and a descendant of the first viscount of Vila Nova de Cerveira, Leonel de Lima. His father was João de Saldanha da Gama (1674–1752), forty-first viceroy of India.
On April 1, 1758, a brief was obtained from the aged Pope Benedict XIV, appointing Saldanha, recommended by the Marquis of Pombal, to investigate allegations against the Jesuits that had been raised in the name of the Joseph I of Portugal.