More than 10,000 people turned out north of Paris on Sunday for a march against Islamophobia two weeks after a man with far-right connections fired shots in a mosque in the southwestern city of Bayonne, injuring two elderly men.

Many of the protesters carried placards denouncing attacks on Islam, a number of women taking part wore traditional Muslim veils, while others had adopted veils bearing the blue, white and red colours of the French flag.

More than 40 percent of Muslims have experienced religious discrimination in France, according to a survey by the French Institute of Public Opinion (IFOP) earlier this month that was cited by Reuters. France has almost six million Muslims, which makes it the second-largest religion in the country and the biggest Muslim community in Europe.

About 13,500 people attended the march, according to a count carried out by the Occurence consultancy and commissioned by the news media, including AFP.

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The march was called by a number of individuals and organisations, including the Collective against Islamophobia in France.

It also came as the debate over the veil has been revived in France and against a background of several attacks in France in recent years.

"We came to sound the alarm, to say there is a level of hate you don't go beyond," one marcher, Larbi, a 35-year-old businessman, told AFP. "We are open to criticism, but you mustn't go beyond certain limits of aggression," he added.

"We want to be heard... not pushed to the edge of society," Asmae Eumosid, a veiled woman from the suburbs of Paris, told AFP.

"You hear a lot of nonsense about Islam and about veiled women today," the 29-year-old added, who works as an engineer in the car industry.

"With or without the veil, we are sick of being the last in line," said a nurse, Nadjet Fella, who said she had campaigned in Algeria against pressure to wear the veil there.

"I chose not to wear it, but it hurts me that those who wear it are picked on," she added.