Ivory Coast has accused French troops of killing unarmed civilians to avenge the death of nine French peacekeepers.
French property in Abidjan was targeted by protesters
Parliament speaker Mamadou Coulibaly said the French had killed 30 people and wounded more than 100 in the main cities of Abidjan and Yamassoukro.
The French have denied this - saying they fired warning shots on protesters near Abidjan airport and a French base.
French citizens were attacked after French forces destroyed five Ivorian government aircraft.
France had responded to an earlier Ivorian air attack on the rebel town of Bouake that left nine French peacekeepers dead - a government breach of a ceasefire signed in July 2003.
The first French troop reinforcements have arrived at Abidjan airport.
Paris has said it is sending more troops and aircraft to the region to stop the escalating violence.
It has 4,000 troops in the country, part of a 10,000-strong UN force mandated to enforce a peace deal between rebels in the north and President Gbagbo's government in the south.
The UN Security Council moved swiftly to back the French action, and called on all sides to stop the fighting.
Groups of Ivorians in Abidjan apparently responded to a call by supporters of President Laurent Gbagbo to retake the airport, which was seized by the French on Saturday.
The BBC's James Copnall in Abidjan said a helicopter flew low over a bridge that splits the city, and fired warning shots as thousands of young men were trying to cross over.
Some protesters ransacked homes of Europeans in the Bietry district of the city as they dispersed.
Earlier, at least two French schools and a library were set alight and French property looted.
Rioters were seen brandishing axes, machetes and clubs as they roamed the streets shouting "French go home!" and "Everybody get your Frenchman!"
A French military spokesman said they had rescued 80-90 French citizens from dangerous situations.
IVORY COAST'S PEACE UNRAVELS
29 Sept: Ivorian parliament fails to agree citizenship laws, which were a key requirement of the January 2003 peace deal
13 Oct: Ivorian rebels say they will not disarm, as planned, until immigration laws are changed
28 Oct: Vendors selling newspapers accused of supporting the opposition are attacked by pro-government militants in Abidjan and southern towns
The New Forces order eight rebel ministers to return to the rebel-held north, saying it had discovered the government smuggling arms across its territory
4 Nov: Government launches air strikes on rebel-held territory in north
5 Nov: More government air strikes and clashes on the ground in north, as unrest erupts in Abidjan
6 Nov: French forces destroy five Ivorian air force aircraft after an air strike leaves French soldiers dead
But Paris strongly rejected suggestions its troops had killed Ivorian civilians.
"Army command denies the report that around 30 Ivorians were killed and another 100 wounded by the French army," said defence ministry spokesman Gerad Dubois, quoted by French news agency AFP.
Explosions and heavy gunfire were also reportedly heard in the capital Yamoussoukro.
President Gbagbo has appealed through a spokesman for an end to attacks on French interests pending an investigation into Saturday's events.
A government spokesman called the air raid in which the French soldiers died a mistake.
An uneasy calm seems to have returned, our correspondent in Abidjan says.
Meanwhile, Paris has dispatched an extra two companies of troops to beef up a force of 4,000 already deployed since the end of the civil war last year.
It has also redeployed three jet fighters to the region.
President Jacques Chirac ordered the "immediate destruction of Ivorian military aircraft used in recent days in violation of the ceasefire".
Paris said it had destroyed two Sukhoi warplanes and three helicopter gunships - virtually the entire Ivory Coast airforce.
The BBC's world affairs correspondent, Mark Doyle, says this is the most serious crisis between France and its former colony since independence in 1960.
Ivory Coast was for many years a tolerant melting pot of religions and ethnic groups, but a coup in 1999 followed by civil war ended all of that with a vengeance, our correspondent says.
Tensions reached boiling point after deadlines for reforms and disarmament designed to lead to peace were missed.
The African Union has urged both the government and rebels to refrain from any further violations of the truce they signed.