The pair, who worked for the Catholic medical charity CODIS, were stopped by four men carrying Kalashnikov rifles in the centre of Bangui as they returned from a town north of the capital, their driver said.
The second aid worker is said to be a local man.
"France condemns this act… and calls for those responsible to free our compatriot as soon as possible," the presidency said in a statement, adding their embassy in Bangui was in contact with the city's archbishop, who has been holding talks with the kidnappers.
The Catholic brother at the wheel of the aid workers' 4×4 said he was robbed by the men who came from the mainly Christian anti-balaka militia, angry at the arrest of one of their leaders by UN peacekeepers on Saturday.
"The three of us were coming from Damara (to the north of Bangui)… when he were stopped by a group of four anti-balaka armed with Kalashnikovs in the middle of the city," Brother Elkana Ndawatcha said.
"They let me go after they robbed me of my mobile telephone, my bank documents and my money. One of them took my place at the wheel and took my colleagues deeper into Boy-Rabe district," one of the anti-balaka strongholds in the northeast of the city.
One person was killed as militia fighters furious at the arrest of Rodrigue Nagibona — known as "General Andjilo" and accused of masterminding massacres of minority Muslims in December 2013 — vented their anger in the district on Sunday night, a police source said.
"Tension is high in Boy-Rabe. One person was shot and killed during the night, and a lot of firing was heard during the night and even this morning," he added.
There were reports of earlier kidnap attempts in Bangui on Sunday.
Violence between rival militias has plunged the deeply poor, landlocked country into bloody chaos.
Mostly Muslim Seleka fighters took power in the majority Christian country in March 2013 before being overthrown by mainly Christian anti-balaka militias. Both sides have been accused of committing atrocities.