Bivugabagabo, who was commander of the operational sector of Ruhengeri, northern Rwanda, during the genocide from April to July 1994, is sought for his participation in the killings.
The arrest warrant was communicated to the French authorities through Interpol.
Biguvagabo, who had been in France for several years, worked in Toulouse for a security company, according to Reuters.
The assistant public prosecutor of Toulouse, Mr Richard Bometon, was quoted to have said that the case is in the hands of the investigation chamber of the Court of Appeal of Toulouse, which will rule on accused's possible extradition.
Two other alleged authors of the genocide, Wenceslas Munyeshyaka and Laurent Bucyibaruta, also arrested in France, have been referred by the international criminal tribunal to France.
The French authorities hold another Rwandan accused of genocide, Dominique Ntawukuriryayo, a former sub-prefect, which the ICTR has requested his extradition.
Another Rwandan naturalized French citizen, Isaac Kamali, is imprisoned in the Parisian area on the basis of a Rwandan arrest warrant after being sent back by the United States.
Â© Hirondelle News Agency