Francois Hollande said one flight data recorder had been recovered, after French troops reached the crash site near Mali’s border with Burkina Faso.
Air traffic controllers lost contact with the plane early on Thursday after pilots reported severe storms.
The 116 passengers on the Air Algerie flight included 51 French citizens.
The McDonnell Douglas MD-83 had been chartered from Spanish airline, Swiftair. It was flying from Burkina Faso’s capital, Ougadougou, to Algiers.
French Interior Minister Bernard Cazeneuve told French radio network RTL that “the aircraft was destroyed at the moment it crashed”.
“We think the aircraft crashed for reasons linked to the weather conditions, although no theory can be excluded at this point,” he said.
A team of 100 French soldiers, with 30 vehicles, had travelled to the crash site on Friday, a French defense ministry official said.
The team was part of a force that was deployed to Mali last year to combat an insurgency backed by al-Qaeda.
“French soldiers who are on the ground have started the first investigations,” Francois Hollande said on Friday.
“Sadly there are no survivors.”
Contact with Flight AH 5017 was lost about 50 minutes after take-off from Ouagadougou early on Thursday morning, Air Algerie said.
The pilot had contacted Niger’s control tower in Niamey at around 01:30 GMT to change course because of a sandstorm, officials say.
Burkina Faso authorities said the passenger list comprised 27 people from Burkina Faso, 51 French, eight Lebanese, six Algerians, two from Luxembourg, five Canadians, four Germans, one Cameroonian, one Belgian, one Egyptian, one Ukrainian, one Swiss, one Nigerian and one Malian.
The six crew members are Spanish, according to the Spanish pilots’ union.
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