DuVall won the open seat four years ago, when Franks walked away from it to run for lieutenant governor on the Democratic ticket.
"I'm humbled by the vote for certain," DuVall said late Tuesday. "Now, my focus will be on winning in November."
Franks said he'll go back to practicing law full time and said, "well, you can't win them all."
DuVall faces Republican Randy Boyd in the Nov. 8 general election. District 19 includes parts of Lee, Itawamba and Tishomingo counties.
With 32 of 32 precincts reporting, DuVall received 62 percent of the vote.
Franks' bid may have been damaged by his public battle with Lee County Superintendent of Education Mike Scott, who admitted months ago to an affair with Franks' now ex-wife.
In the region's other runoff races for Democratic nominees to the Legislature, late-night totals were slow and results close.
In District 13, with 26 of 31 precincts reporting, Billy Gray of Hickory Flat held a slim lead over Don Randolph of Holly Springs.
Randolph led the vote in a five-candidate field Aug. 2.
The winner will face Republican Steve Massengill of Hickory Flat in November. The district includes parts of Benton, Lafayette, Marshall and Union counties.
The post was vacated when longtime Democratic incumbent Jack Gadd of Hickory Flat opted to run for superintendent of education.
In District 4, with 27 of 29 precincts reporting, Jody Steverson of Ripley held a narrow lead over James Nunnally of Ripley, who barely missed winning the primary Aug. 2.
This winner will face Republican James Benefield of Ripley. District 4 consists of Tippah and parts of Union and Benton counties.
The seat came open when Democratic incumbent Greg Ward of Ripley announced his retirement.
The region had no GOP runoffs for the Legislature.