McEnery was born in Monroe, Louisiana. He attended Spring Hill College in Mobile, Alabama, the United States Naval Academy in Annapolis, Maryland, and the University of Virginia at Charlottesville. In 1859, McEnery graduated from the State and National Law School in Poughkeepsie, New York. McEnery served as a lieutenant in the Confederate States Army during the U.S. Civil War.

In 1866, McEnery began practicing law in Monroe. He was elected Lieutenant Governor in 1879, and became Governor of Louisiana in 1881 after the death of Louis A. Wiltz. McEnery was elected to a full term as governor in 1884, but failed to be re-elected in 1888. McEnery's administration was weak due to the power held by the State Treasurer Edward A. Burke and the Louisiana Lottery Company through corruption.

After losing the 1888 election, McEnery was appointed to serve as an associate justice in the Louisiana Supreme Court. He was elected to serve in the United States Senate in 1896, serving there until his death in 1910. While in the Senate, McEnery served on the Committee of Corporations formed in the District of Columbia and the Committee of Transportation and Sale of Meat Products.

McEnery died on June 10, 1910 in New Orleans, Louisiana and was interred there in the Metairie Cemetery.