Police have fired tear gas to disperse hundreds of demonstrators in the Comoran capital, Moroni.
Crowds chanted anti-French slogans near France's embassy after a renegade leader, Colonel Mohammed Bacar, fled to the French-run island of Mayotte.
Col Bacar fled the island of Anjouan after government troops and an African Union force invaded the island.
He has asked France for asylum, but the Comoran government and the AU have asked France to extradite him.
The African Union's special representative for the Comoros, Francesco Maedeira, has called on France to recognise that Col Bacar is a political criminal and to hand him over to the Comoran authorities.
French officials have said he could be charged with illegally entering France's territory and weapons possession after he is transferred to the island of Reunion, reports the AFP news agency.
The operation against Col Bacar was launched after he refused to step down as president of Anjouan, and accept the authority of the federal government after a disputed election last year.
The BBC's Jonny Hogg in Moroni says the embassy is being protected by armed Comorian police, keeping the crowd some 200m away.
Anyone who appears to be French is being targeted with one group of young men making throat slitting gestures as they march past whilst others threw stones, our reporter says.
One government official told the BBC "if France is seen to be protecting Mohamed Bacar, God knows what will happen to their representatives here ''.
The island of Mayotte is the only one of the Comoros islands to have opted to remain French when the other islands gained independence in 1975 - but it remains a source of contention with both countries claiming sovereignty.
The BBC's Jonny Hogg says Col Bacar's arrival on the island follows reports last week that he had received backing from individuals on Mayotte during the eight-month political stand-off.
The government in the Comoros has expressed disappointment that he was able to flee to Mayotte.
A government spokesman warned that if Col Bacar was not returned to face justice it could cause a diplomatic crisis.
"We have notified France that we want Colonel Mohamed Bacar and all the fugitive rebels to be extradited to Comoros," acting Foreign Affairs Minister Houmadi Abdallah told reporters.
"We reminded the French authorities ... that the international arrest warrants against them are still in effect."
On Wednesday, the Comoros authorities appointed a new transitional leader for Anjouan - the vice-president of the Comoros, Ikililou Dhoinine.
"Ikililou Dhoinine will be the political authority in Anjouan until a transitional government is set up," a government spokesman told the AFP news agency.
Mohammed Desara, the Comoran chief of defence staff, said troops were continuing to pursue elements loyal to Col Bacar and secure the island fully.
It is not known how many people died in the fighting but Mr Desara said it was certain that at least some of Col Bacar's fighters had been killed.
About 600 Comoran and AU troops landed in an amphibious assault as dawn broke on Tuesday.
Residents of the island were pictured greeting the government forces with jubilation as they patrolled the streets.
The Comoros archipelago in the Indian Ocean has had a fractious history since independence from France, experiencing more than 20 coups or attempted coups.
The three main islands of the archipelago - Grand Comore, Moheli and Anjouan - lie 300km (186 miles) off Africa's east coast, north of Madagascar.