The woman was pulled over by police and told that her face veil 'reduced her field of vision' behind the wheel.
She insists that she could see 'perfectly well' and may sue the police after accusing them of discrimination.
"I unveiled myself so I could be identified. He had no right to give me a penalty notice," The Sun quoted the unnamed woman, as saying.
"It was discrimination, pure and simple," she added.
Her lawyer Jean-Michel Pollono added, "We live in a free country and wearing a full-face veil is still legal."
However, a Nantes police spokesman insisted the woman's clothing presented a 'safety risk'.
The incident has provoked outrage in France, where critics of government policy say that it is a symptom of the 'burqa hysteria' generated since some politicians first called for a ban on the full body veil.
Muslim women are required to wear burqas and in some cases facial veils as they are not allowed to show their faces in public.