The rise of Saint-Denis France means the flight of the Jews. Since 2000, when banlieue anti-Semitism began to flare alongside the Palestinian intifada, the number of Jewish families in Aulnay-sous-Bois fell from 600 to 100, in Le Blanc-Mesnil from 300 to 100, in Clichy-Sous-Bois from 400 to 80, and in La Courneuve from 300 to 80. French Jews call this flight internal aliyah.

This is why they move: in 2014, 51 per cent of reported racist incidents in France targeted Jews. On average a Jew is assaulted in France every day. And this means it touches most families. A recent poll found that 74 per cent of Jews who wore traditional skullcaps and 20 per cent who didn’t reported being attacked.

Madame Saada’s community is a refuge: in 2000 it was 800 families strong, now internal aliyah has enlarged it to 1,500. This crush makes the synagogue feel more like a home than a place of worship. And, like so many things Jewish, it is a cacophonic mess: someone is looking for a tennis racket, a flotilla of pastry boxes seems to be arriving, and the rabbi is nowhere to be seen. It seems so similar to Jewish life in London — but then 20 soldiers arrive. “I’m the next guard,” booms a tall white trooper with a buzz cut.

Since the jihadi slaughter at the HyperCacher after the Charlie Hebdo attack last year, 10,000 troops and 5,000 police have guarded all Jewish sites in France. The military has been brought in because there are now so many potential jihadist cells and lone wolves in the banlieue that there is simply no other way to protect them.

Mme Saada looks at the troops. Every day she sees the uniforms and feels amazingly thankful and amazingly sad. It has come to this: that the Jews are, once again, so hated that they need the army patrolling their every building to keep them safe. It feels, almost, like a return to the Middle Ages, when the Jews were protected by the prince and would avoid those areas where the writ of their sovereign was weakest. French Jews with a sense of humour joke about their protector as le Prince Valls, Prime Minister Manuel Valls, and how they avoid banlieues where his rule is weak.

“It’s traumatic, claustrophobic, to live every day,” she says, “with soldiers, seeing we are so hated we can’t be here without them. It’s particularly awful at the school gates, thinking that without the army our children would come home dead.” Many pious ones, who, praying daily, almost live in the synagogue, really struggle. At least in Israel the soldiers are not at the door.

She turns round and calls to a veiled cleaner in Arabic — help me tidy up. This is typically French Jewish. Mme Saada was born in Tunis. France’s Jews are some 70 per cent Sephardic: they were once the Jews of French Algeria, Morocco and Tunisia. Theirs is a newer, bigger, poorer community than Britain’s. “We arrived speaking Arabic,” she says, “in the same banlieues as the Arabs. We used to wish each other happy holidays. But things turned violent.” Moving away from this is bankrupting many families.

Mme Saada is growing old, but her eyes are wide brown. “This future frightens us. We’re being marginalised.” Three children have moved to Israel, two to New York. Only one is left in Paris. “We didn’t even get one full generation in France.”

At the edge of Seine-Saint-Denis, I am sitting in the functional, plastic-grey office of Jérôme Fourquet. This slight, dark-haired man is one of France’s most famous pollsters. Given that the state forbids ethno-religious statistics, he laughs that his work is skirting the edge of the law.

“Statistics show,” he says, “perceptions of anti-Semitic insecurity exploded in France in the early 2000s. This reconfigured where French Jews live.” They are not moving far. Half of France’s roughly 500,000 Jews live in the Paris conurbation. This aliyah is from one banlieue to another. “We found that the number of Jews in districts of Seine-Saint-Denis has plummeted in ten to 15 years.”