Laurent Fabius said the crew of Air Algerie flight AH5017 requested to return to Burkina Faso after initially asking to change course due to bad weather.
The plane’s two flight data recorders have arrived in France.
The jet was flying to Algeria when it crashed in Mali, killing all 118 aboard, including 54 French citizens.
France has taken the leading role in the investigation.
“What we know for sure is that the weather was bad that night, that the plane crew had asked to change route then to turn back before all contact was lost,” Laurent Fabius said on Monday.
A team of French investigators is currently sifting through the plane’s wreckage in Mali, but Laurent Fabius said they were facing “extremely difficult conditions”.
“It’s a long, fastidious and extremely complex job,” he added.
French, Malian and Dutch soldiers from a UN peacekeeping force (MINUSMA) have secured the site, about 50 miles south of the Malian town of Gossi, near the Burkina Faso border.
Earlier on Monday, a French official confirmed that the two flight data recorders had arrived in France and were now being examined by experts.
One of the devices was retrieved almost as soon as rescuers arrived on the spot, while the second was found late Saturday.
A source close to the investigation told the AFP news agency that one of them was badly damaged on the outside.
Martine Del Bono, a spokeswoman for the French aviation investigation office, refused to comment on their condition, telling press: “At this stage, we cannot say anymore.”
Even if both “black boxes” are in good condition, French Transport Minister Thierry Mariani has warned that analyzing the flight data and cockpit conversations could take “weeks”.
French flags were lowered to half-mast on Monday for three days in memory of the dead.
Nearly half of those on board were French. There were also 27 from Burkina Faso and further passengers from, among others, Lebanon, Algeria, Canada and Germany.
Among the French contingent on board flight AH5017 was a family of 10.
The plane, a McDonnell Douglas MD-83, had been chartered from Spanish airline Swiftair and all six members of the crew were Spanish.
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