Much of the violence, that has left an estimated 465 dead in the past week, has eased since the arrival of French troops but reporters in the capital, Bangui, yesterday saw a mosque burning, houses looted and cars set on fire.
Residents reported several lynchings overnight.
CAR has descended into chaos since mainly Muslim Seleka rebels seized power in March. Months of looting, raping and killing since has brought reprisals by Christian militias.
Michel Djotodia, Seleka leader-turned interim president, has lost control of his fighters, many from Sudan and Chad.
The soldiers’ deaths in Bangui were announced just before French president François Hollande’s office said he would make a stop-over there on his way back from a memorial service for the late Nelson Mandela in South Africa.
“The head of state expresses his deep respect for the two soldiers’ sacrifice,” his office said.
The 1,600-strong French force battled gunmen in Bangui on Monday in a bid to disarm rival Muslim and Christian gunmen. Soldiers have also been deployed to other towns across CAR, where a regional African peacekeeping force has struggled to stamp its authority.
French officials said on Monday night they had restored some stability to Bangui although shooting had broken out when gunmen refused to hand over their weapons.
The two French soldiers, marine paratroopers from the 8th regiment based in Castres, died after coming under attack at close range during an overnight patrol, the government said.
According to Celestin Christ Leon, for the African peacekeeping force in Bangui, a rebel commander was harassing people, who called on the French to help. “They came and tried to disarm the Seleka but gunfire erupted,” he said.
Mr Hollande rushed French troops to CAR last Thursday immediately after the UN Security Council authorised France to use lethal force to help African peacekeepers restore order.
An attack on Bangui by Christian militia, known as “anti-balaka” and some fighters loyal to deposed president François Bozize triggered the latest violence. Tens of thousands of Christians have fled reprisals by Seleka gunmen following the offensive, but the French move to disarm all fighters has weakened Seleka’s influence in the capital.
In the Fouh neighbourhood, civilians armed with wooden clubs and machetes yesterday attacked a mosque and nearby houses. “We found arms in their mosque. We don’t want to see Djotodia and his Muslims here any more,” said one man at the scene, who wielded a knife.
At least six people were lynched overnight, mainly during violence targeting Muslims, according to residents.
The French presence on Bangui’s streets was lighter than on Monday, when disarmament operations were under way.
CAR is rich in diamonds, gold and uranium, but its people remain poor and the country has seen little stability in decades.