The city was attacked, reportedly by militias loyal to Francois Bozize, who was ousted as president by rebels in March, plunging the country into chaos.
The UN Security Council has now voted to allow French troops to join an African peacekeeping force in the CAR.
The violence has raised fears of mass killings along sectarian lines.
French Foreign Minister Laurent Fabius told the BFM-TV news channel that the French deployment would total around 1,200, with 600 troops already in place.
The UK military says it is discussing “limited logistical support” for the French mission in the CAR but will not send combat troops.
About 250 French troops were sent out onto the streets of Bangui when the violence began on Thursday.
The Security Council resolution also imposed an arms embargo and asked the UN to prepare for a possible peacekeeping mission of its own.
The BBC’s Andrew Harding, in Bangui, reported seeing many people lying wounded in the halls of a hospital.
Our correspondent says the violence in the CAR is increasingly pitting Christians against Muslims.
Michel Djotodia, who ousted Mr Bozize, installed himself as the first Muslim leader in the Christian-majority country.
The mainly Muslim Seleka rebel coalition which brought him to power has been accused of atrocities against Christians.
Christian communities have now set up so-called “anti-balaka” self-defence forces, most of them loyal to Mr Bozize.
“Balaka” means machete in the local Sango and Mandja languages.
The Selekas have been officially disbanded and some of them integrated into the army, but correspondents say it is often not clear who is in charge, even in the capital.
A Seleka general told the BBC there were 54 bodies lying in a mosque in Bangui. BBC journalists saw another 20 to 30 bodies lying in the streets outside.
CAR Prime Minister Nicholas Tiangaye, in Paris for a Franco-African summit, called for the immediate deployment of French troops.
He blamed Thursday’s violence on the “anti-balaka” militias.
The UN special representative in the CAR, Babacar Gaye, told the BBC there was a danger of mass killings in Bangui if nothing was done to stop the violence.
“Today something very worrisome happened because a group… attacked the town.
“We don’t know the size, but what we know is that within ex-Seleka [rebels], casualties have been observed including commanding officers and we know that downtown, unfortunately, targeted violence is ongoing, so we are in a very bad situation,” Mr Gaye said.
Our correspondent says Bangui is quieter than it was when the fighting began on Thursday morning, with only the occasional burst of gunfire.
He says the attack looks like an attempt to change the balance of power before the French intervene but for now, Seleka forces remain in control.
An existing peacekeeping force about 2,500 strong, the International Support Mission in Central Africa (Misca), is already in place.
It is now under a 12-month UN mandate and will rise to some 3,600 African soldiers, in addition to the 1,200 from French forces.
About 10% of CAR’s 4.6 million people have fled their homes, the UN says.