Ten members of the same French family were among the 118 victims of the Air Algérie plane crash on Thursday, the third air disaster in a week.

The victims were three generations of the Reynaud family from the Rhône Alpes region of France.

Michel Reynaud, his former wife, their two sons, two daughters-in-law and four grandchildren were all on flight AH5017. The group had been attending a family wedding in Burkina Faso.

“It’s a tragedy. It was the holiday of a lifetime for them,” a grieving friend told the French newspaper Le Dauphiné Libéré.

Another victim, Bertrand Gineste, 55, died along with his wife Véronique and their three children.

“He was my best friend, my brother,” his business partner Jean-Jacques Dupré told AFP. Dupre and Gineste jointly owned a pharmacy in the central French town of Gueret, where residents were numbed by the tragedy.

Amadou Ouedraogo, a Burkinabe who has been living in France for 30 years, was mourning seven family members.

The plane was carrying “my brother, his wife, their four children and another nephew, the son of my sister,” he said.

“They made the effort to take their children to discover their roots and look what happens,” he said. “We just want to know what happened.”

One Nigerian who is yet to be identified died in the crash.

Details of many of those killed when flight AH5017 came down in the desert in Mali were released on Friday. Humanitarian workers, tourists and expatriates were among those flying from Burkina Faso, where the plane left for Algiers in the early hours of Thursday. Many were to meet connecting flights to Europe.

Of those who died, 54 were French, and the country’s president, François Hollande, described it as a tragedy for the “whole French nation … and others.”

A military drone identified the crash site at Gossi, near the Burkina Fasoborder, and soon after French forces in the area secured the zone and confirmed there were no survivors.

The wreckage of the aircraft, much of it in small pieces, was spread over a relatively small area and one of the plane’s flight recorders was found quickly and sent for examination. France has also sent an air investigation team to the scene.

Footage of the crash scene was shown on French television on Friday night. From the sky all that can be seen is a blackened crater in the sand. On the ground, the debris suggests the plane fell like a stone from the sky hitting the ground at huge speed.

Witnesses said there were “no seats, no luggage, no trace of human beings” and the plane looked as if it had been pulverised.

After a crisis meeting at the Elysée on Friday morning, Hollande confirmed that all 118 people on board – 112 passengers and six Spanish crew – had perished. Earlier reports had put the number of people on the flight at 116.

“Sadly, there are no survivors,” Hollande told journalists. He said the foreign minister, Laurent Fabius, would receive the victims’ families on Saturday and would be given “all the information they need.”

“My thoughts are with the victims and their families. We stand at their side,” he said.

He said atrocious weather conditions in the region were believed to be the most likely cause of the accident, but added: “No hypotheses has been ruled out … it is still too soon to draw any conclusions.”

Fabius said the area where the wreckage had been found was “savannah and sand” and that the rainy season was complicating the search operation.

“The aim is to return the bodies to the families as soon as possible,” he said.

Gilbert Djendéré, a presidential spokesman in Burkina Faso, said: “The plane completely disintegrated [on impact].” A minister who spoke on condition of anonymity said: “There are no phone lines in Gossi, which is why it was so difficult to confirm any information. It was nomads who saw the plane falling during the night, and they alerted the Burkinabe army.”

Gossi is 90 miles (140km) from the strategic garrison town of Gao, where many of the 1,600 French troops in Mali as part of Operation Serval are based.

The sparsely populated town, which is inhabited mainly by nomadic Tuaregs, was the scene of some of the fiercest fighting in northern Mali during 2012, when Islamist extremists took control of much of the region. Fifty Malian soldiers were killed during clashes between the army and Tuareg rebels in May.

About 40 minutes after flight AH5017 took off from Ougadougou, the capital of Burkina Faso, the pilot asked to change his flight path to avoid heavy storms. The aircraft disappeared from the radar shortly afterwards, and it was only after the plane failed to arrive as scheduled in Algiers that it was announced missing.

The French transport minister, Frédéric Cuvillier, said the accident was probably due to “extremely bad weather conditions.”

“Was that the sole cause, or was there a technical problem, which compounded the situation? That we will have to find out,” he said.

•Adapted from a Guardian of London report. Photo, courtesy Jean-Sebastien Evrard/AFP/Getty Images, shows Amadou Ouedraogo, a Burkinabe who lost seven family members in the Air Algerie crash.