A Democrat, Broussard was born in Calcasieu Parish, of which Lake Charles is the principal city, to Dosety Broussard and the former Elvina Lyons. He relocated to Lafayette with his widowed mother in 1870. He was educated in public schools.
Broussard served as sheriff from 1888 to 1904, when he was badly defeated in a bid for re-nomination, then the equivalent to reelection in Lafayette Parish. His administration worked to guarantee continued Democratic hegemony in Lafayette when Fusionists, or dissident Democrats and Republicans with African-American backing, unsuccessfully challenged the majority party in the late 1890s. In 1897, his deputies captured the notorious murderers, Alexis and Ernest Blanc, who were subsequently executed in 1897.
On November 13, 1890, Broussard married the former Debbie Dougherty, one of the founders of the First Baptist Church of Lafayette. He died in Lafayette and is interred at the Protestant Cemetery in the majority Roman Catholic city.
- Broussard, Isaac A.. Louisiana Historical Association" A Dictionary of Louisiana Biography.. Retrieved on March 12, 2020.
- Sheriffs of Lafayette Parish, 1888-1976.