The son of Solomon DesBrisay, and his wife, Mary Campbell, he was a descendant of Captain Théophile de la Cour DesBrisay (1671–1761) whose Huguenot family fled religious persecution in France and settled in Dublin, Ireland before emigrating to Canada. Alexander DesBrisay was born in Bathurst, New Brunswick and educated at a public school.
After graduating from West Tennessee College, he studied law at Lebanon Law School.
He was a lawyer in Tennessee before and after the war, mayor of Jackson, Tennessee, 1856, and an unsuccessful candidate for the Democratic Party nomination for governor of Tennessee in 1880. He was elected mayor of Jackson, Tennessee in 1856. Alexander William Campbell enlisted in the Confederate States Army as a private.
On or about May 9, 1861, he was appointed major and assigned to duty as assistant inspector general of the Provisional Army of Tennessee.
He was promoted to colonel of the 33rd Tennessee Volunteer Infantry Regiment on October 18, 1861. Campbell"s regiment was in reserve at the Battle of Belmont.
Campbell led his regiment at the Battle of Shiloh. He was severely wounded during the battle.
After several months convalescence, he returned to find that he had not been re-elected colonel of the regiment on its reorganization on May 8, 1862.
Upon his return to active duty, just before the Battle of Stones River, Campbell was appointed assistant adjutant and inspector general for Lieutenant General Leonidas Polk. After this assignment, he served with the Tennessee volunteer and conscription bureau under Brigadier General Gideon Pillow. Sent on a mission for Tennessee Governor Isham G. Harris to supervise elections and to recruit new soldiers in the western part of Tennessee, Campbell was taken prisoner by Union forces at Lexington, Tennessee in July 1863.
He was not exchanged until February 1865.
On February 18, 1865, Campbell was appointed acting inspector general for Lieutenant General Nathan Bedford Forrest. Later in the month, according to Sifakis, or on March 1, 1865, according to Eicher, Campbell was given command of a brigade in Brigadier General William H. Jackson"s division of Lieutenant General Forrest"s cavalry corps, with which he served until the end of the war.
On March 1, 1865, Campbell was commissioned as a brigadier general in the Confederate Army. He was paroled at Gainesville, Alabama on May 11, 1865.
After the Civil War, Campbell returned to Jackson, Tennessee and resumed his practice of law.
He also was engaged as a banker. He unsuccessfully sought the Democratic Party nomination for governor of Tennessee in 1880. He died on June 13, 1893 at Jackson.
Alexander William Campbell was buried in Riverside Cemetery, Jackson, Tennessee.
A supporter of the Province of New Brunswick joining the proposed Canadian Confederation, in the February 21, 1865 New Brunswick general election, DesBrisay was voted into office as the Confederation Party representative for Restigouche County in an election won by an Anti-Confederation Party made up of a coalition of Conservatives and Reformers led by Albert J. Smith. DesBrisay was reelected in the 1866 New Brunswick general election won by his party.
