Catherine Samba Panza's appeal to the former colonial power came three days after France's decision to boost its contingent to 2,000 and on the eve of a review of the deadly sectarian conflict by the UN Security Council.
"The interim president told us that they should stay until the elections, that is to stay until early 2015," French MP Elizabeth Guigou said in Bangui yesterday.
When France launched operation Sangaris in December to prevent mass sectarian killing, President Francois Hollande envisioned a short deployment.
The French parliament is due to vote on February 25 on whether the 2,000 troops deployed in Central Africa can stay longer than their initial mandate, which expires in April.
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The right-wing opposition has asked for clarity on the operation's goals but stopped short of calling for an early withdrawal.
"France cannot handle everything on its own," Guigou, a Hollande ally who chairs the parliament's foreign affairs committee, said after her meeting with Samba Panza.
"To achieve a nationwide footprint we need an international contingent of at least 10,000," Denis Sassou Nguesso, the president of the Republic of Congo, told French newspaper Le Figaro in an interview.
Amnesty International said last week that the mostly Christian anti-balaka vigilantes were attempting to exterminate the country's Muslim minority.
"'Ethnic cleansing' of Muslims has been carried out in the western part of the Central African Republic, the most populous part of the country, since early January 2014," Amnesty International said in a report.
With the remnants of Seleka on the back foot since France deployed its forces two months ago, most of the ongoing violence is now blamed on the anti-balaka's attacks.
Samba Panza, a Christian who took over as interim president last month from ex-Seleka boss Michel Djotodia, has said she was "going to go to war against the anti-balaka.