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Her slain husband, bombed-out Damascus home and refugee life are behind her. The recipient of a coveted asylum-seeker visa, Syrian teacher Amena Abomosa is settling into a new life in France with her family. But now what?

They are among the few amid a sea of desperate Syrians to arrive in Europe with prior approval to seek haven. British Prime Minister David Cameron and other European leaders would prefer for all refugees to come this way - applying at European embassies abroad, undergoing careful screening and entering the EU legally. Everyone else, they argue, should stay away, instead of risking perilous journeys.

Those fleeing Syria's war don't want to stay away, and demand for special asylum visas far outstrips supply.

And even those fortunate enough to have the proper paperwork and persistence to win those visas face challenges in their new European homes.

After flying to France last month from Jordan, the Abomosas were sent to a spartan transit center full of other refugees. Lacking French or English, they missed the train they were meant to take to their new home. And Abomosa, a former middle school science teacher, was unable to get medical attention for her 62-year-old mother, suffering from half-treated colon cancer.

Still, Abomosa, her mother Hanna, teenage daughters Isra and Reemaz, and 12-year-old son Muhammad are hopeful, and grateful.

"I'm entering the unknown," she said from a Paris train station, en route to her new home, smiling and choking up at the same time. She dreams of returning to Syria one day, but knows that day will not come soon. "I only want stability for my children."

They fled Syria in 2013 for Jordan, where they watched conditions deteriorate recently. Abomosa and her oldest daughter found work, but struggled to get paid. Recent cuts in international aid have pushed many Syrian refugees to gamble on deadly smuggling routes to Europe — or even to risk returning home.

Abomosa saw that only as a last resort. She painstakingly compiled paperwork to seek an asylum visa — birth certificates, school and medical records.

Almost by miracle, she succeeded. France issued just 985 such direct-settlement visas last year. Syria's war has sent 4 million people fleeing. Abomosa lists off her many friends who've tried repeatedly and failed to win such a visa.

"I have an idea about France and its people, they are sophisticated, they have subtlety, they are agreeable," she said. "That's my idea of this country."

So far, that dream hasn't been punctured.

"My daughters absolutely wanted to see the Eiffel Tower," she said — and now they have. Amena, 18-year-old Isra and 17-year-old Reemaz slipped away from the transit center briefly to visit the tower, the Arc de Triomphe, the Champs-Elysees.

Isra giggled about Paris pigeons and showed off selfies they shared on Facebook with Syrian friends now scattered in Jordan, Germany, Sweden. In her suitcase, she has a photograph of her father — "God bless him" — her diary, a teddy bear and sand from home.

Compared to countless Syrians entering Europe on dubious boats and crossing treacherous land borders, the Abomosas arrived in relative luxury, landing in a French government-funded flight in Paris' Charles de Gaulle airport.

The transit center where they ended up in the Paris suburb of Creteil was "disappointing," with tiny, old rooms, collective kitchens and bathrooms. And the inability to communicate makes them all vulnerable.

But it's a world away from the barbed wire on Hungary's border or the filthy camps in the French port city of Calais where migrants gather before trying to sneak across the Channel to Britain.

France's asylum system is among Europe's most troubled, with long delays, a high refusal rate and applicants often left homeless while they wait for responses. The government is trying to fix it, amid Europe's worst migrant crisis in generations, and the Abomosas' experience is a rare sign of progress.

After a couple of weeks in the transit center, they set off for the Brittany town of Vannes, where they will live in public housing while their asylum procedure runs its course.

Maud Mignard, a social worker in charge of Abomosa family, said, "We are here to make them discover the 'user's manual' (of France), explain how things work here, give them keys to success so they can manage themselves."

They may be welcomed, or not. The increasingly popular far-right National Front is tapping into and fueling anti-immigrant sentiment in communities across France.

Abomosa isn't concerned. "I don't reproach them with anything. Certain Arab countries don't want us either. Why do you want me to reproach Europeans?" she asked.

The French she's met so far "are very helpful. They don't have a racist spirit."

Her greatest concern is getting medical attention for her mother, who started chemotherapy after a colon operation but had to interrupt it because of fighting in Damascus, and vomits regularly without explanation.

Abomosa herself has deep scars circling her abdomen from when Syrian soldiers forced their way into her home and the door handle and glass ripped into her torso.

She shrugs off that injury, but loses her composure when talking about her husband, Abdul Arrzaq Mardini, 48, killed in 2012 outside their home while trying to help an injured child. Both died. The scene was filmed and then broadcast on Roya TV. Abomosa said her husband took no sides in the war and was killed for no reason.

That loss, Abomosa said, hardened her resolve to find safety for her family.

"I had to do something. I feel responsible," she said. "They need the important things, food, shelter, a daily life."

Speaking of food, she described a French apple pastry she'd long wanted to sample. "I've heard many things about French cooking," she said with a smile.

Will she seek out fellow Syrians in France for companionship, advice? Probably not. "I have nothing to do with politics, and I don't want to," she said. She insists her family took no sides in the civil war, and is afraid of being associated either with Islamic State extremists or Syrian President Bashar Assad.

"We came to France with the hope that my children will continue their studies, their future... that they will have a decent, respectful life," she said.

When the family at last reached Brittany, a new problem greeted them. The social workers sent to meet them spoke no Arabic.

But they found haven: a three-bedroom apartment in a housing project in a calm corner of town, arranged by non-profit groups working to help refugees.

Her children will attend special language-intensive classes, and the family should have access to basic medical care and receive a small monthly stipend.

Abomosa wants to return the favor soon.

"This is a new life and a future. We don't want to feel that we only receive, we also want ... to give."

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Sylvie Corbet in Paris contributed.