French Interior Minister Claude Gueant says six women have been convicted and fined since a ban on face-covering Islamic veils took effect in April.
Gueant cites the figure in an interview with "Le Monde" daily, saying no woman has been sent to a citizenship class -- another potential punishment.
Controversy surrounded the law's passage.
Muslim leaders say it stigmatizes all followers of Islam.
Backers say the law is aimed at ensuring France's secular values and gender equality and nipping radical Islam in the bud.
compiled from agency reports