Mr. Abraham received just shy of 24 percent of the vote, trailing Mr. Rispone by three percentage points. He conceded on Saturday night and endorsed Mr. Rispone.

Mr. Rispone, who with his brother founded an industrial engineering, construction and maintenance company in Baton Rouge, had aligned himself with Mr. Trump’s policies, particularly on immigration, and had attacked Mr. Abraham for being, in his view, inconsistent in his support for the president. Mr. Rispone emphasized the dearth of his political experience throughout the campaign as he sought to portray Mr. Edwards and Mr. Abraham as career politicians.

“This is just the first step,” he said in a speech on Saturday night. “We’re going to be the governor of Louisiana. We’re going to turn this state around.” He said that the president had called to congratulate him, prompting his crowd of supporters to chant “Trump!”

Mr. Edwards was first elected, in part, because of the dismay stirred by the huge structural deficits left by Mr. Jindal, who pushed for tax cuts and tax breaks that failed to stimulate the economy. But Mr. Edwards also benefited after his 2015 opponent, Senator David Vitter, was hobbled by a prostitution scandal.

Republicans have called Mr. Edwards an “accidental governor,” and he is one of very few to hold the top office in the Deep South. But competitive, closely watched races in Mississippi and Kentucky have Democrats hoping to claim states in the heart of Trump country.

In Mississippi, Jim Hood, a Democrat who has won four consecutive terms as the state attorney general, is competitive in the governor’s race. And in Kentucky, Gov. Matt Bevin, a Republican, ranks in polls as one of the least popular governors in the country, bolstering the prospects of Andy Beshear, the state attorney general and son of the former Democratic governor Steve Beshear.

Speaking at a rally on Friday night in Lake Charles, La., Mr. Trump sought to lump Mr. Edwards with leaders from the national Democratic Party, like Speaker Nancy Pelosi and Senator Chuck Schumer, the minority leader.