Irina Belenkaya was arrested in Hungary on Sunday night while attempting to cross the border to Ukraine with her daughter.
Elise Andre, who was snatched from her father last month, returned to France on Monday.
Russia's foreign minister said on Tuesday that Hungary had taken a "hasty" decision in returning Elise to France. Sergei Lavrov said the Foreign Ministry would take steps to protect the interests of "Russian nationals Irina and Liza."
In France, Belenkaya is also accused of organizing an attack on the girl's father, Jean-Michel Andre. Andre says his ex-wife was among a group of assailants who seized his daughter from him.
Elise has been 'kidnapped' back and forth three times in the past two years by her warring parents. Andre, who was awarded custody by a French court after their divorce in 2007, is wanted in Russia, where Belenkaya has been granted custody of the girl.
Belenkaya demanded in court on Wednesday that Elise be returned to her.
"French authorities have no right to seize my child from me!" she also said, accusing her ex-husband of preventing her from contacting their daughter.
Belenkaya's lawyer, Robert Fridman, said that extradition could take 60 days, as his client had rejected a simplified extradition procedure.
"In this time period we hope we will be able to influence the French authorities to review their decision [on Elise]," Fridman said.
Andre said on Wednesday his lawyer would travel to Moscow in the next few days to study the Russian kidnapping case against him. He said travel expenses would be covered by the Russian side.
