The girl was last seen in a park Sunday evening, The Local.fr reported. When her mother was unable to find her, she alerted police.
A search for the girl has been carried out by soldiers, firemen and police reinforcements, who have focused their efforts on the park.
However, with growing concern for Fiona's safety, authorities asked Monday that anyone who was in the park and may have taken photos or videos on their mobile phones contact police.
Fiona, who is blonde and about 3.6 feet tall, was last wearing a black track suit which had the white logo "Hello Kitty" on it. She was also wearing black athletic shoes and a gold chain around her neck, police said.