"At dawn (Thursday), an armed pick-up opened fire three times in the direction of civilians and French troops. After the third time, we retaliated and destroyed the vehicle," said the spokesman for the French general staff, Colonel Gilles Jaron.
He said such pick-up trucks, often equipped with mounted machine guns, usually carry four or five occupants.
There were no injuries or deaths among the civilians or soldiers, Jaron said.
Several hundred civilians had fled to near the airport overnight on Thursday to benefit from the protection of about 400 French troops stationed there.
Jaron said about 2,000 civilians were in the area on Thursday.
The clash took place before the UN Security Council gave a green light for a mission that will see France send an additional 600 troops to the African country, doubling the force it already has in and around the capital.
The resolution authorized the deployment of up to 3,600 African and 1,200 French troops to try to contain violence in CAR that erupted after a March coup.
On Friday during a two-day summit in Paris, French President Francois Hollande told African leaders it is time for their continent to take charge of its own security as a major summit went ahead against the sombre backdrop of mourning for Nelson Mandela.
"Africa is not free until it is totally free from insecurity, from wars, from underdevelopment, from poverty and inequality.
"This is the befitting tribute to Madiba, to... continue on this journey of discussing how we should continue working together to find African solutions to African problems."