The women, part of a demonstration that erupted in front of Notre Dame cathedral here, were detained for taking part in an unauthorised protest rather than for wearing their veils. But, in theory at least, French officials can now slap fines on Muslim women who refuse orders to expose their faces when in public.

“Today was not about arresting people because of wearing the veil. It was for not having respected the requirement to declare a demonstration,” said police spokesman Alexis Marsan.

Two women in niqabs, a woman wearing an Islamic headscarf that did not cover her face and a protest organiser were arrested, Marsan said.

Separately, businessman and activist Rachid Nekkaz said he and a woman friend of his wearing the niqab were arrested by the police in front of President Nicolas Sarkozy’s Elysee Palace.

“We wanted to be fined for wearing the niqab, but the police didn’t want to issue a fine,” said Nekkaz, who has promised to auction off a two-million-euro property to start a fund to pay off fines for veil-wearers.

One of those arrested in front of Notre Dame was 32-year-old Kenza Drider from the southern city of Avignon, who was due to appear on television and has become a symbol of France’s tiny community of niqab wearers.

“This law infringes my European rights, I cannot but defend them, that is to say my freedom to come and go and my religious freedom,” Drider told reporters as she boarded a train for Paris before the protest.

Many French police fear the law will be impossible to enforce, since they have not been empowered to use force to remove head coverings, and could face resistance in already tense immigrant districts.

“The law will be infinitely difficult to enforce, and will be infinitely rarely enforced,” said Manuel Roux, deputy head of a union representing local police chiefs.

“It’s not for the police to demonstrate zeal,” he said, predicting that when patrol officers meet veiled women, they will simply try to explain the law to them and to persuade them to remove their face covering. “If they refuse, that’s when things get really complicated. We have no power to force them,” he said. “I can’t begin to imagine we are going to pay any attention to a veiled woman in a sensitive area, where men are proud.”

The law came into effect at an already fraught moment in relations between the state and France’s Muslim minority, with Sarkozy accused of stigmatising Islam to win back votes from a resurgent far right.