Why has the refusal of France to grant a passport to an Algerian woman who declined to shake the hand of a state official at her citizenship ceremony because of her "religious beliefs" made the BBC website? Picked up by other news' outlets, including the New York Times, it's not unreasonable to infer that the subtext is: there go the French again, discriminating against Muslims. If it's not the burka or the burkini, it's a handshake.

But why would any western country welcome a woman who shuns one of its oldest and most courteous customs? If she finds shaking hands with a man beyond the pale, one is entitled to suspect she may not look too favourably on gays and Jews. Anti-Semitism is now so profound in France that on Sunday 250 well-known figures, including Nicolas Sarkozy and Manuel Valls, signed a letter warning that the country's Jews are victims of "ethnic purging" at the hands of "radical Islamists".

Government posters are a common sight in France, reminding all citizens that it is against French law to cover one's face in public. They say: 'La République se vit à visage découvert' [The Republic lives with its face uncovered]. Nonetheless, a small number of women continue to defy the law, such as the one in Toulouse who refused to show her face to police when asked last Sunday. She then insulted the police and was arrested, sparking three days of rioting by local youths.

Of course, there are plenty of Muslims who are fully integrated into French society. But life is not always easy for them. Emmanuel Macron has been talking much in recent weeks of his determination to tackle what he calls the "underground Islamism" that seeks to "corrupt". The first victims of the extremists are their fellow Muslims, the millions of men and women perfectly well integrated but facing daily intimidation by the Islamists, who assault them ideologically, trying to undermine their faith with accusations of apostasy for daring to dress in a skirt or wear shorts on the football pitch. The latter is becoming a problem in some inner-city Muslim-majority football clubs, where male players are encouraged to wear leggings instead of shorts, whatever the weather, in order to preserve their modesty.

The 'radicalisation' of sport in France is a growing concern, with one report last year estimating that the number of young people radicalised in sports' clubs was 863. Most are men, for the simple reason that women aren't welcomed in sports associations infiltrated by Islamists. A recent report on French television revealed what had been happening at a wrestling club in Toulouse; four years ago the club boasted 58 male members and 10 females, but there are now 69 men and one woman. One of the women who left the club, Julie, explained her decision: "The club president told me: 'When you're wrestling and your t-shirt pulls up, and we can see your skin and your stomach, that disturbs some people'." The final straw for Julie was when one of her wrestling partners, a boy, told her he could no longer train with her "because my religion forbids me from touching women".

Predictably, the disclosure that France has denied citizenship to the Algerian woman has been greeted with much indignation from around the world. But in rejecting her application, the French have demonstrated that they won't tolerate the intolerance of extremists.