Francis entered Harrow School early in 1818, and matriculated from Oriel College, Oxford, on 12 November 1824, graduating B.A.
On 4 June 1829, he entered Lincoln's Inn with the intention of studying law, but in 1834 he was ordained deacon and became curate of St. Giles, Reading.
On 6 December 1837, he married Mary Caroline (d. 1886), daughter of William Marsh, honorary canon of Worcester.
By her, he had a son, Richard William Francis (1849–1860), and two daughters, Mary Melesina and Maria Marcia Fanny.
Trench's chief works were: He also issued in 1869 and 1870 a series of miscellaneous papers, entitled Islipiana.