Randolph ran for a seat in the United States House of Representatives in 1982 and 1992, losing both campaigns.

In 1997, Randolph lost a bid for a seat on the Louisiana Circuit Courts of Appeal.

An outpouring of remembrances by members of the Louisiana House of Representatives, Louisiana State Senate, former governors, Governor John Bel Edwards, and numerous other former and current local, state, and national public servants followed.

[3][4] On November 27, 2018, the Alexandria City Council voted to name the downtown convention in Randolph's honor to focus upon the late mayor's emphasis on economic development.

First opened in 1996 with a price tag of $17.2 million, of which $13 million was state funded, the center has more than 67,000 square feet of events space and is connected to the Hotel Bentley and the Holiday Inn Downtown.