Close was born on 11 July 1797 in Frome, Somerset, the youngest son of the Rev. Henry Jackson Close, who was at one time Rector of Bentworth, near Alton, in Hampshire. Enrolling at St. John's College, Cambridge in 1816 he earned a Bachelor of Arts in 1820, and was elevated to MA in 1825. During the same time period, he was ordained a deacon in 1820, and as a priest the following year. In 1822 he was assigned as curate of Willesden and Kingsbury in the London area. Two years later, in 1824, he was assigned to Cheltenham and the parish church of St Mary's, and when the rector died in 1826, he was elevated to that office.
Close served as rector for thirty years, where he was a popular preacher and a noted evangelical. He was a vociferous opponent of the Oxford Movement. He advocated for the creation of a training college for schoolteachers and opposed alcohol, tobacco, horse racing and theatrical amusements. He was involved in the provision of new churches in Cheltenham. On 24 November 1856, he was nominated to be Dean of Carlisle Cathedral by the Prime Minister, Lord Palmerston, and the appointment was approved by the Queen. That same year, the Archbishop of Canterbury conferred a Lambeth Doctorate of Divinity upon Close. He remained as Dean of Carlisle until 1881, when failing health forced him to resign. At the time of his resignation, he was the oldest of all deans in the Church of England He died in Penzance the following year, on 12 December 1882, and was buried in Carlisle Cathedral.
Close married twice; in 1820 he married Anne Diana Arden, and in 1880 Mary Antrim.
Close was the author of around seventy books and pamphlets, though by 1887 few were considered "of any permanent value." In 1885 a marble statue of Close was installed in Carlisle Cathedral, after a public collection of funds for the purpose. Dean Close School and Francis Close Hall, both in Cheltenham, were named in his honour.
- Crockford's Clerical Directory 1881
- "THE DEATH LIST OF A DAY; A VENERABLE ENGLISH CLERGYMAN DEAD". The New York Times. 19 December 1882. p. 5. Retrieved 17 February 2010.
- "Close, Francis (CLS816F)". A Cambridge Alumni Database. University of Cambridge.
- "The Late Dean of Carlisle". Marlborough Express. XVII (297). New Zealand. 20 December 1882. p. 2. Retrieved 17 February 2010.
- Boase, George Clement (1887). . In Stephen, Leslie (ed.). Dictionary of National Biography. 11. London: Smith, Elder & Co. pp. 123–124.
- "No. 20521". The London Gazette. 28 October 1845. p. 3227.
- "No. 21944". The London Gazette. 25 November 1856. p. 3919.