Claiborne was named after Jean François Hamtramck and was the son of Ferdinand Claiborne. He was also a nephew of William Charles Cole Claiborne and Nathaniel Herbert Claiborne, grandnephew of Thomas Claiborne, great-grandfather of Herbert Claiborne Pell, Jr., great-great-grandfather of Claiborne de Borda Pell, and great-great-grand-uncle of Corinne Claiborne Boggs.
He was admitted to the bar in 1825, and commenced the practice of law at Natchez. He was a member of the state House of Representatives from 1830 to 1834, then moved to Madison County, Mississippi, and was elected as a Jacksonian to the Twenty-fourth Congress, where he was a Representative from March 4, 1835 to March 3, 1837.
Claiborne presented credentials as a member-elect to the Twenty-fifth Congress and served from July 18, 1837, until February 5, 1838, when the seat was declared vacant as the result of a contested election. He then engaged in newspaper work in Natchez. In 1844, he moved to New Orleans, Louisiana and resumed newspaper interests.
He was appointed United States timber agent for Louisiana and Mississippi in 1853. He was the author of several historical works including his 1880 History of Mississippi.
- United States Congress. "John Francis Hamtramck Claiborne (id: C000404)". Biographical Directory of the United States Congress.
- John Francis Hamtramck Claiborne at Find a Grave
- Life of J. F. H. Claiborne (1903), by Franklin Lafayette Riley
- Mississippi, as a province, territory, and state : with biographical notices of eminent citizens