The demonstrators say France, the former colonial power, has done little to deter rebels who have taken over large parts of the country’s east and north.
“France has a tendency to abandon us,” a protester told news agency AFP. “We no longer need France. France may as well take its embassy and leave.”
The French ambassador says the protests sere “particularly violent”.
Vincent Floreani, the deputy spokesman for the French Foreign Ministry, confirmed several protesters entered the embassy’s gardens by “jumping over a fence”, but they were pushed back.
He says France is supporting efforts at political dialogue by countries in the region.
Most of the protesters were reportedly youths close to the country’s ruling party, the Kwa Na Kwa, and the embattled President François Bozizé.
AFP reports the offices of Air France were also attacked.
The instability caused Air France to order its weekly Wednesday flight from Paris to Bangui, which departed just before 11am Paris time, to return to the French capital.
The rebels, known as the Séléka alliance, have in recent weeks taken a string of towns in the country's north.
They took control of the central town of Kaga Bandoro on Tuesday despite the presence there of troops from neighbouring nations meant to shore up the weak national army.
They are now reported to be advancing towards Bangui.
“We call on the boys and girls of the Central African Republic, on defence and security forces still loyal to the regime of François Bozizé…to lay down their arms immediately,” Séléka announced in a statement.
The rebels, who have so far encountered little resistance from the army, said that, “by the measure of security and the protection of civilians, we don’t consider it necessary to launch a battle for Bangui and send troops there, because General François Bozizé…has already lost control of the country.”
Séléka took up arms on 10th December, saying the government has failed to respect peace accords signed between 2007 and 2011 which offered financial support and other help to insurgents who laid down their arms.
Bozizé came to power in 2003 after a brief war and has repeatedly relied on foreign interventions to fend off rebellions and the spill-over from conflict in neighbouring Chad and Sudan.