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The BBC's Hugh Schofield said Kenza Drider's protest successfully captured public attention and registered an objection to the law
At least two women have been detained in France while wearing Islamic veils across their faces, after a law banning the garment in public came into force.
Police said they were held not because of their veils but for joining an unauthorised protest against the ban.
France is the first country in Europe to publicly ban a form of dress some Muslims regard as a religious duty.
Anyone caught breaking the law will be liable to a fine of 150 euros (£133; $217) and a citizenship course.
People forcing women to wear the veil face a much larger fine and a prison sentence of up to two years.
It was not clear whether the women detained at the protest would also be fined for their veils.
They had taken part in a demonstration outside Paris' Notre Dame cathedral. Police said the protest had not been authorised and so people were asked to move on. When they did not, they were arrested.
"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.
Under the law, any woman - French or foreign - walking on the street or in a park in France and wearing a face-concealing veil such as the niqab or burka can be stopped by police and given a fine.
It is a small fine, but symbolically this is a huge change, says the BBC's Hugh Schofield in Paris.
Guidelines issued to police say they should not ask women to remove their veils in the street, but should escort them to a police station where they would be asked to uncover their faces for identification.
The French government says the face-covering veil undermines the basic standards required for living in a shared society and also relegates its wearers to an inferior status incompatible with French notions of equality.
The ban on face coverings - which does not explicitly mention Islamic veils, but exempts various other forms - has angered some Muslims and libertarians.
A French Muslim property dealer, Rachid Nekkaz, said he was creating a fund to pay women's fines, and encouraged "all free women who so wish to wear the veil in the street and engage in civil disobedience".
Mr Nekkaz said he and "a female friend wearing the niqab" were arrested at a separate demonstration 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," he told the AFP news agency.
In the southern city of Avignon a woman boarded a train wearing a niqab - as she had long declared she would - unchallenged by police.
"It's not an act of provocation," said the woman, Kenza Drider.
"I'm only carrying out my citizens' rights, I'm not committing a crime... If they ask me for identity papers I'll show them, no problem."
But opposition protests by Islamists and libertarians are unlikely to make much of an impression, our correspondent says.
What is more open to question, he says, is whether an out-and-out legal ban is necessary when, on most estimates, only 2,000-or-so women in France actually wear the niqab or burka.
Critics of French President Nicolas Sarkozy say it suits him to play up the Muslim question because he is an unpopular president in need of an easy vote-winner.
Muslim headscarves
- The word hijab comes from the Arabic for veil and is used to describe the headscarves worn by Muslim women. These scarves come in myriad styles and colours. The type most commonly worn in the West is a square scarf that covers the head and neck but leaves the face clear.
Are you in France? What is your reaction to the ban? Does a face-covering veil undermine the basic the standards required for living in a shared society, as the French government claims? You can send us your views and experiences using the form below.