Paris (CNN) -- April in Paris. The flowers are blooming, the sun is shining and Parisiens are out on the Champs Elysee enjoying the warm weather.

In the plaza at the front of the Notre Dame Cathedral, teeming with camera-toting tourists, two French women step out wearing the niqab -- the full Islamic face veil that reveals only the eyes. As of Monday, that is officially breaking the law.

It didn't take long for this small protest to become a scene. A media scrum of jostling cameras and microphones soon grew around them blocking the already hectic pedestrian traffic.

Curious tourists began snapping pictures without even knowing what they were photographing. "Who is it? Is it Britney Spears?" one excited girl asked harried journalists. Hmm, not quite.

Police moved in with about 20 or so uniformed officers, several police vans and a number of plainclothes security personnel with walkie talkies. There was a lot of confusion and a some slightly panicked calls to superior officers to control the situation

Because it's one thing to ban the burqa and the niqab: It's another thing to enforce it.

Police guidelines say face veils must not be forcibly removed. Rather, any police officer encountering a veiled woman public should give her a warning, ask for her to identify herself by removing her veil and, if she refuses to do so, bring her down to the police station for a possible euro 150 fine and perhaps a course of French culture and values.

But how many cops on the beat are really going to bother confronting veiled women -- especially when there are only between 500 and 2,000 in the whole country?

At Notre Dame, the two women were arrested -- but not for wearing the niqab. Police said they were charged with staging an unregistered protest. Either way, the women made their point, veil or no veil.

Parisiens observing the scene seemed bemused. One woman didn't even know the law was going into effect today.

A young man was irritated by the law, saying it might lead to Muslims being further stigmatized and, worse, citizens conducting their own punitive actions against veiled women.

Another couple sitting nearby the scene grumbled that the women "should go back" to where they came from. Which in the case of many veiled women would be ... France.

Far from Notre Dame, in a well-to-do suburb of Paris, Hind Amas wears long black gloves and the niqab. All you can see is her Kohl-rimmed eyes.

She's a single mom, a bit harried from looking after her rambunctious three-year old daughter. She's articulate and opinionated. It's hard to imagine anyone forcing her to do anything.

She's happy to remove her veil to identify herself at the school her daughter attends or other offices. But she plans to defy the law by wearing her veil to the park and on the street.

But she's not too worried. By now, the neighborhood has gotten used to it. Even the local baker, who recognizes her by her voice, has assured her she will be supported by the community.

After all, she says, she's not so different from her neighbors. "The only thing is the veil. It's this veil that disturbs people. That I wear three grams of material."

She shrugs watching her daughter in a sleeveless, pink sun dress race through the playground, "To each what they will."