Conceição's victory, following a fast-paced third round that lifted enthusiastic Brazilian spectators from their seats, gives the host country a shot at its first Olympic boxing gold.
Oumiha, a 21-year-old from Toulouse, now faces the challenge of defeating Conceição for the title on his home turf.
"He is in his home country but for me that won't make it more difficult," Oumiha said. "I won't let my guard down and I won't stop believing that I can win."
If he were to prevail, it would be France's first gold boxing medal at the Games since 2000.
Conceição, a 27-year-old from the northeastern city of Salvador, was eliminated in early stages of the last two Olympics. On Sunday, though, he won a unanimous decision against Cuban world champion Lázaro Álvarez.
The Brazilian said he is more focused and driven, especially on a Sunday that happens to be Father's Day in Brazil, after the birth of a daughter in 2014.
"I even disconnected from social media," he said, underscoring his single-minded focus on winning. "I promised my daughter that I would fight for a medal for her."
Tension between the two boxers' staffs following the fight prompted a shouting match in front of reporters after a Cuban coach complained the Brazilians were celebrating too loudly.
At the London Olympics in 2012, Brazil won a silver and two bronzes.
(Reporting by Paulo Prada and Pedro Fonseca; Editing by Neil Robinson and Meredith Mazzilli)
