Islamic State insurgents seized large swathes of northern Iraq last month, prompting hundreds of Christian families in Mosul to flee a city which has hosted the faith since its earliest years.
"We are providing aid to displaced people fleeing from the threats of Islamic State and who have sought refuge in Kurdistan. We are ready, if they wish, to facilitate their asylum on our soil," France's foreign and interior ministers said in a joint statement.
"We are in constant contact with local and national authorities to ensure everything is done to protect them."
Iraqi Prime Minister Nuri al-Maliki earlier this month condemned the treatment of the Christians and instructed a government committee to help those made homeless. However, he has not said when the army might try to win back control of Mosul.
Islamic State has warned all women in Mosul to wear full-face veils or risk severe punishment. The Sunni insurgents, who have declared a caliphate in parts of Iraq and Syria, also view Iraq's majority Shi'ites as infidels who deserve to be killed. REUTERS