Faulcon was born on February 8, 1841, in Surry County, probably into slavery and almost certainly of mixed-race ancestry. He was the son of Nancy Lunsford and Jacob Faulcon. As a young man he trained as a blacksmith. Faulcon also received some education and learned to read and write. The circumstances of when and how he gained his freedom were not recorded. In 1863 Faulcon married Rebecca Jane Hargrave, though legal unions between enslaved persons were not recognized until after the Civil War. They had at least six children, of whom only one son and one daughter survived infancy.
After the Civil War, Faulcon operated a blacksmith shop near Surry Court House, and in May 1879 he purchased fifty acres of land one mile south of the town. He acquired an additional ten acres in 1881 and a neighboring thirty acres in 1884. He was among a group of African American legislators and businessmen who in January 1886 incorporated the Colored Agricultural and Industrial Association of Virginia to establish an annual fair to exhibit farm and industrial products. A successful entrepreneur, Faulcon lent money to his relatives and neighbors throughout the decade. By 1890 his household furnishings included a clock, a sewing machine, and $20 worth of musical instruments.
Becoming involved in politics after the war, in October 1871 Faulcon attended a meeting of Republicans to nominate a candidate for the Senate of Virginia from the district comprising Petersburg and the counties of Prince George and Surry. It is not known whether he had any connection with the Readjusters, a coalition of blacks and whites formed later in the decade who supported paying only a portion of the state’s antebellum public debt and who in 1884 merged with the Republican Party. In September 1885 Faulcon attended a meeting of local Republicans called to select a candidate for the Senate of Virginia. At another convention on September 22, a large majority chose him as the party’s nominee for a seat in the House of Delegates. Although the Democratic Party cemented its majority in the General Assembly and reclaimed the governorship from the Republicans at the election on November 3, Faulcon easily defeated his Democratic opponent by a vote of 2,079 to 1,330.
Representing the counties of Prince George and Surry, Faulcon took his seat when the assembly opened on December 2. During the session of 1885–1886 and the extra session of 1887 he served as a low-ranking member on the Committees on Executive Expenditures, on Immigration, and on Public Property. During the first session Faulcon did not make formal remarks or introduce any legislation. He joined the minority in voting for William Mahone, leader of the Republican Party in Virginia, when the assembly elected John W. Daniel to the U.S. Senate. During the extra session Faulcon presented several bills on behalf of Surry County residents, including one to incorporate a local railroad. He was not a candidate for reelection in 1887, although in 1891 he was the Republican nominee for the district’s seat in the House of Delegates. He withdrew shortly before election day, however, following controversy about his nomination within the party. Faulcon continued to participate in politics, and in September 1898 was a delegate to the Republican convention that nominated the party’s candidate for the House of Representatives from the Second Congressional District.
Faulcon’s wife died in 1887 or 1888, and on October 3, 1888 he married Martha Jane Elliott. They did not have any children before her death on July 16, 1889. Faulcon married Ida Pretlow on December 10, 1890. They had three daughters and two sons. He continued to farm on his ninety-acre tract in the Cobham district of Surry into the twentieth century. Faulcon died on an unknown date probably not long before April 9, 1904, when the Surry County Court ordered the appraisal of his estate. His burial place is not known.
