Duvall won the contest four years ago to replace Franks, who gave up the post to seek statewide office.
Tuesday, DuVall narrowly led the balloting with 44 percent across parts of Lee, Itawamba and Tishomingo counties, edging Franks with 33 percent.
The runoff winner will meet Republican Randy Boyd in the Nov. 8 general election.
DuVall and Boyd are from Mantachie.
Meanwwhile, in House District 17, Lee County Rep. Brian Aldridge of Tupelo won 68 percent of the vote to defeat second-time challenger Michael Stafford in the GOP primary. Aldridge wins re-election without opposition in November.
Franks of Mooreville walked away from his House seat to run for lieutenant governor on the 2007 Democratic ticket. Now practicing law in Tupelo, he's also chairman of the state party.
Franks' campaign to regain the seat may have been tinged somewhat by his very public legal threats against Mike Scott, Lee County's superintendent of education, who admitted a sexual affair with Franks' now-former wife.
In Tuesday's primary, Duvall got 1,928 votes compared with Franks' 1,467. Brad Underwood of Mantachie came in third with 990 votes or 23 percent.
A highly watched race outside Northeast Mississippi saw challenger Chris Massey unseat GOP Sen. Doug Davis of DeSoto County for the District 1 seat. The Democrats failed to field a candidate, so Massey will go to Jackson in January.
Davis is the current chairman of the powerful Appropriations Committee, but he's become a target in Republican crosswinds between lieutenant governor candidates Billy Hewes of Gulfport, Davis' political ally, and Tate Reeves of Flowood, who's said he favors Sen. Merle Flowers in the money post.
Across Northeast Mississippi, contests fought for 11 House and two Senate seats. Five incumbent House members and two incumbent senators will go back to Jackson without primary or general election opposition.
The region has 24 House seats and 10 Senate seats out of a total 122 in the House and 52 in the Senate.
Seven incumbents chose not to seek re-election.
Runoffs appeared likely in several races, including to succeed longtime Rep. Jack Gadd in District 13 and Rep. Greg Ward in District 4.
One of the region's most-watched contests is for Senate District 8, held for many years by Jack Gordon of Okolona. Gordon died earlier this year.
In its two party contests, incomplete returns showed Democrat Russell Jolly leading, and a dead-heat between Republicans Patsy Gregory and Victor Horn.
Gordon's successor won't be known until the general election contest is over.
Political observers predict the outcome of this region's House elections is key to which party controls the House of Representatives. Its most powerful leader, the speaker, will be elected by the membership in January.
The current speaker, Billy McCoy of Rienzi, chose not to seek re-election in District 3 after decades in the House and two terms as speaker.
Replacing him will be either Tommy Cadle, a Democrat who won outright in a three-man contest Tuesday, or Republican William Tracy Arnold.
One high-profile race not on the ballot until November is for the Senate District 9 seat held three terms by Oxford attorney Gray Tollison.
He'll face former Ole Miss football player Todd Wade, a Republican.