In a joint statement with the Interior Minister Laurent Fabius said: "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".
Thousands of Christians have been forced to leave their homes in Iraq because of an ultimatum given by Islamist militants last week.
ISIS, which has taken over large parts of the country, warned them to pay a tax, convert or face death.
The statement also said the French government was "in constant contact with local and national authorities to ensure everything is done to protect" Christians.
Last week the Iraqi Prime Minister Nuri al-Maliki condemned ISIS for its treatment of Christians: "What is being done by the Daesh terrorist gang [ISIS] against our Christian citizens in Ninevah province, and their aggression against the churches and houses of worship in the areas under their control reveals beyond any doubt the extremist criminal and terrorist nature of this group," he said.