the town of Sevare, about 610 kilometres (380 miles) north of the capital Bamako.
The building, originally meant to provide shelter to passing truckers, now serves as their home.
Sevare has never changed hands or fallen to the Islamist radicals but is close to many towns and villages which have.
Mariam Sisoko, a 27-year-old mother-of-three whose last child Ibrahim was born here, comes from Gossi, 420 kilometres east of Sevare.
"Thanks to the French army and thanks to all the French," she says, beaming. "In one month, or two or three, we will, thanks to God, be able to return home."
Mali's former colonial master France launched a military intervention in the sprawling west African country on January 11 to counter a push southwards by al-Qaeda-linked Islamists occupying the arid north since April.
The campaign, now buttressed by the arrival of African forces, has seen the recapture of key central towns in a major boost for the morale of Malian troops who failed to offer any real resistance to the invaders.
Sisoko says the news of the Islamist reverses has sent hopes soaring.
"Ever since we learnt about the French offensive, we have been preparing our bags," she says.
"We just have a few clothes," she says. "The moment the war is over, we go home."
The man in charge of the camp is a 55-year-old former car mechanic named Boakar Traore, who calls himself Blake after a character in a US television series.
Traore, who ran a garage in Hombori, 320 kilometres east of Sevare, fled when it was taken by Tuareg rebels from the MNLA, a separatist group that wants to carve out an independent homeland called Azawad.
"They attacked my garage. They wanted the car spare parts but above all wanted to take me hostage to repair their Toyotas," he said.
"Now it's the Ansar Dine who are holding Hombori," he said, referring to the Defenders of Faith, an Islamist group linked to al-Qaeda, who chased out the Tuaregs.
"I have two workers who remained there and they were forced to work for them," Traore said. "At least the bearded men pay a little bit. The MNLA don't give money at all. It's slavery," he said.
"I go to church and to the mosque and believe that all roads lead to God," Traore said. "And that is something these people detest. They killed the village chief, a man who was for us like God."
Children run around the vast courtyard of the building, where there is a school. Food supplies are provided by the Malian government, along with the UN World Food Programme and Catholic charities.
Adama Toure, 24, says more than 30 members of his family from the northern region of Gossi are all here.
"When we left, the truck driver wanted us to pay 10,000 CFA francs (15 euros/$20) per person," he said. "We didn't have money, it took us a month to repay him by doing odd jobs here."
An old woman, weaving a little girl's hair into thin long braids, said: "Even though they razed our homes and there is nothing left, we must go back. For us that's home, no other place will do."