A more familiar explanation for French antagonism to the facial veil is historical and political: the deep-rooted French fear, resentment and rejection of the “other” — the immigrant, the invader, the potential terrorist or abuser of human rights who eats, drinks, prays and dresses differently, and refuses to assimilate in the French way. Some of the French, particularly on the far right, still believe that France’s colonial “civilizing mission” was a noble one, and that the people of former colonies, including the Arabs of North Africa, have clung to backward ways that they are now exporting to France. “The veil’s presence reminds French people daily that that mission failed,” said Rebecca Ruquist, an American scholar of race and religion in modern France. “It has been seen as a sartorial rejection of the values of the French republic.”

By donning an all-encompassing black garment that covers all but the eyes, these women seem to want their coverings, not their faces, to be noticed. Their veils are generally fixed in place, cut or shaped in such a way that they hide all but their eyes.

In some parts of the Islamic world, however, women opt for more fluidity. In Saudi Arabia, for example, where Muslim women are required to keep their bodies and hair under wraps in public, facial covering is neither obligatory nor banned and can be used in a kind of cat-and-mouse game with strangers. One favorite head covering is a long black scarf that becomes opaque when doubled over. It is worn with one end hanging down in front, the other over the shoulder. Should a strange man look at her, a woman might take the hanging end of the scarf and flip it up to cover her face. She can see out, but no one can see in.

France’s officials and legislators have used an amalgam of arguments to defend their new law. Interior Minister Claude Guéant said it defends “two fundamental principles: secularism and the principle of equality between man and woman.” A stronger argument is that any hidden face is a potential security risk, and it is on that basis that the law does not single out Islamic veils by name, but rather all facial coverings in public.

In theory, that means that anyone wearing a balaclava, a fencing mask or a motorcycle helmet with a full-face visor could be punished. But will they? The French might be shocked if they were. And there are exemptions, for Santa Clauses and carnivalgoers, for example.

Here’s another question: Will lavish-spending female tourists from gulf Arab states be forced to bare their faces on the Champs-Elysées? (In Switzerland, Justice Minister Eveline Widmer-Schlumpf wants to ban facial veils, but has said that gulf tourists will be exempt.) Perhaps, as some have suggested, it will be rare for anyone to be penalized in France, given how difficult it is to enforce the law fairly and uniformly.