Rwanda has broken off diplomatic ties with Paris, in a row over a French inquiry related to the 1994 genocide.
President Kagame has always accused France over the genocide
The government has recalled its envoy to Paris and given the French ambassador to Kigali 24 hours to leave.
A French judge issued warrants two days ago for the arrest of nine aides of the Rwandan leader over his predecessor's killing - which sparked the genocide.
Rwanda has accused Paris of trying to destabilise its government. France said it regretted Rwanda's move to cut ties.
Paris has insisted the French judge, Jean-Louis Bruguiere, acted on his own authority and in total independence.
Issuing the warrants, Judge Bruguiere accused President Paul Kagame - who under French law has immunity as head of state - of ordering the former president's death. Mr Kagame has denied involvement.
More than 800,000 people died in the 100-day massacres of Tutsis and moderate Hutus which followed the killing of the ethnic Hutu President Juvenal Habyarimana.
The French allegations have sparked anger in the Rwandan capital, Kigali, where about 25,000 people reportedly took part in a government-organised demonstration against France on Thursday.
The Rwandan government has said the French ambassador to Kigali must leave within 24 hours. Other French diplomats have 72 hours to go.
ARREST WARRANTS ISSUED
James Kabarebe, military chief-of-staff
Charles Kayonga, army chief-of-staff
Faustin Nyamwasa-Kayumba, ambassador to India
Jackson Nkurunziza, working for presidential guard
Samuel Kanyamera, RPF deputy
Jacob Tumwime, army officer
Franck Nziza, presidential guard officer
Eric Hakizimana, intelligence officer
Rose Kabuye, director general of state protocol
Foreign Minister Charles Murigande earlier told AFP news agency that Kigali had recalled its ambassador to Paris as the ministry did not "see why he should be there at this point".
"France is intent on destroying our government, we do not see any need for keeping any relationship with a hostile country," Mr Murigande said.
BBC world affairs correspondent Mark Doyle says the only surprise about Rwanda's decision to break off diplomatic relations with France is that it has not come earlier.
Mr Kagame's Tutsi-dominated Rwandan Patriotic Front (RPF) - effectively the government - has had appalling relations with Paris for over two decades, he says, and whatever the quality of the French judge's evidence, the whole affair was always going to be deeply politicised.
The French foreign ministry said in a brief statement that Rwanda's decision to break off diplomatic ties would take effect from Monday.
"We regret this decision. We are making all necessary arrangements," it said.
Speaking earlier on Friday, a spokesman had said Paris had no intention of recalling its own envoy to Kigali and wanted to keep dialogue open.
Judge Bruguiere is investigating the case because the crew of the plane were French and their families filed a case in France in 1998.
Thousands turned out to protest against France
Those he wants to arrest include armed forces chief James Kabarebe and army chief-of-staff Charles Kayonga.
Judge Bruguiere has said that only Mr Kagame's Tutsi-dominated Rwandan Patriotic Front (RPF) forces had missiles capable of downing President Habyarimana's plane.
He said the attack was carefully planned by the RPF.
Mr Kagame has denied this, describing suggestions that he was behind the assassination of the former president as scandalous.
He has always accused France of having links to those who carried out the genocide.
After Habyarimana's plane crashed, Hutu extremists started massacring ethnic Tutsis and Hutu moderates.
The genocide came to an end when Mr Kagame's then rebel RPF seized power 100 days later.
The RPF has always said the Hutu extremists shot down the presidential plane to provide a pretext to carry out the genocide.