The investigation chamber of the Court of Appeal of Toulouse requested additional documents from the Rwandan legal authorities before considering the extradition request.
Mr Bivugabagabo, 53, was arrested in Toulouse on 7 January on an international arrest warrant issued by Rwandan Attorney General.
The accused was employed as a guard in a security company and has been living legally in Toulouse for several years.
His name appears in a list of the 93 people wanted by Rwanda for genocide.
Meanwhile, the investigation chamber of the Court of Appeal of Paris will on 20 February render its decision on the transfer warrants to the International Criminal Tribunal Rwanda (ICTR) of priest Wenceslas Munyeshyaka and the former mayor, Laurent Bucyibaruta.
© Hirondelle News Agency