Born near Boonesborough, Kentucky, French attended private schools. He studied law. He was admitted to the bar in 1820 and commenced practice in Winchester, Kentucky. He served as member of the State house of representatives 1820–1826. He served as judge of the circuit court in 1829.
French was elected as a Jacksonian to the Twenty-fourth Congress (March 4, 1835 – March 3, 1837). He was an unsuccessful candidate for reelection in 1836 to the Twenty-fifth Congress. He was an unsuccessful Democratic candidate for Governor of Kentucky in 1840.
French was elected as a Democrat to the Twenty-eighth Congress (March 4, 1843 – March 3, 1845).
French was again elected to the Thirtieth Congress (March 4, 1847 – March 3, 1849). He resumed the practice of law. He died in Covington, Kentucky, on May 1, 1854. He was interred in the family burial ground near Mount Sterling, Kentucky.