"If there is an African candidacy for the position of secretery-general of La Francophonie that would make a lot of sense," Macron said at a press conference with Kagame. "If that candidacy is African and feminine that would make even more sense."
French support for Mushikiwabo is thus part of Macron's strategy of maintaining French economic and cultural influence in Africa, where he sees the most promising future for the French language.
Along with Kinyarwanda and Kiswahili, French is an official language in Rwanda, a former Belgian colony.
But it is only spoken by 5.6 percent of the population and was replaced as a teaching language by English in 2008.
While remaining a member of La Francophonie, Rwanda has also joined the Commonwealth.
The French decision is a blow to Canada, which after the announcement stood by incumbent Michaëlle Jean, a Haitian-born Québecoise who has been criticised for big spending on decorating her official apartment and endorsing elections in Africa that some campaigners considered undemocratic.
Speaking to RFI's sister TV station France 24, Rwandan Foreign Affairs Minister Louise Mushikiwabo announced that Kagame had invited Macron to visit the country, describing the invitation as "an important gesture".
The last visit by a French leader was when Nicolas Sarkozy went there in 2010.
Macron said on Wednesday he will do what he can to improve relations with Rwanda, though the two countries have not fully normalised ties.
Bilateral relations have become strained with Rwanda accusing France of complicity in the 1994 genocide, accusations Paris denies.
Kagame and Macron were both to attend the VivaTech fair in Paris on Thursday, following Macron's meeting with tech moghuls on Wednesday.