The magazine said Juppé "has long been considered hostile to the current authorities in Kigali."
Juppé, who was also foreign minister during the Rwandan genocide in 1994, has said he will not "shake hands" with Kagamé or go to Rwanda following the release of a 2008 report accusing France of complicity in the genocide.
Juppé, who has dismissed the report as "lies and fabrications", did not meet his Rwandan counterpart when she visited France and was outside the country during Kagamé's visit.
Despite differences over the choice of a new envoy, French foreign ministry spokesman Vincent Floreani said he two countries had a good relationship.
"Relations between France and Rwanda have not stopped strengthening since the visit of the president to Kigali in February 2010, which sealed at the highest level the political and economic recovery between our two countries," he said.
Contini, considered close to former foreign minister Bernard Kouchner, fell out of favour with Juppé last year after making statements considered too favourable to Kigali.
France and Rwanda have a history of difficult ties and relations between the two countries were broken off between 2006 and 2009.
Tensions have eased this year after experts mandated by a French inquiry to probe the 1994 downing of Rwandan leader Juvenal Habyarimana's jet cleared Kagamé's aides of involvement.
The assassination of Habyarimana was one of the triggers that unleashed a genocide that left around 800,000 Rwandans dead.
Following the 1994 attack, hardliners from the slain president's Hutu ethnic group, led by members of his inner circle, began to slaughter members of Kagamé's Tutsi minority.
Kagamé's rebel FPR eventually managed to overthrow the Hutu-led regime.