The warrants follow suits filed separately by the former spouses of the couple. They are believed to have taken with them four girls aged between three and five.
The first suit was filed by Ilham Tarbouni, who had no news of her three-year-old daughter after she went to her father's home for the summer.
Police went to the home of the father, a Muslim convert, and found it empty.
The 34-year-old had allegedly professed his intention to go to Saudi Arabia or Iraq.
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Like a number of European countries, France has expressed concern over radicalised young people leaving the country to fight in Iraq and Syria, and who could pose a risk to domestic security on their return.
In France, about 950 people are thought to fight or have fought in Syria, to have returned or be in the process of going there.