Francis Edward Joseph Mostyn was born in Talacre, Flintshire, Wales, the fourth son of Sir Pyers Mostyn, 8th Baronet (1811–1882; see Mostyn Baronets) and Frances Georgina (née Graser; died 1899), and was ordained to the priesthood on 14 September 1884. On 4 July 1895, he was appointed the first Vicar Apostolic of Wales and Titular Bishop of Ascalon by Pope Leo XIII.
He received his episcopal consecration on the following 14 September 1895 (the ninth anniversary of his priestly ordination) from Cardinal Herbert Vaughan, with Bishops John Carroll and John Hedley, OSB, serving as co-consecrators. He was later named Bishop of Menevia upon his vicariate’s elevation to a diocese on 14 May 1898. On 7 March 1921, Mostyn was appointed Archbishop of Cardiff by Pope Benedict XV, leading the only Roman Catholic Archdiocese in Wales. He died in 1939, aged 79, having served as Archbishop for eighteen years.