French President Francois Hollande said he believed none of those on board the A320 had survived, while the head of Lufthansa spoke of a dark day for the German airline, Censor.NET reports citing Reuters.
"There were 148 people on board," Hollande said. "The conditions of the accident, which have not yet been clarified, lead us to think there are no survivors."
French officials said there were 142 passengers and six crew on board and the plane issued a distress call at 0947 GMT, about 52 minutes after take-off.
Hollande said there was likely to be a significant number of Germans on the flight from Barcelona to Duesseldorf.
He added: "The accident happened in a zone that is particularly hard to access."
It was the first crash of an airliner on French soil since the Concorde disaster just outside Paris in July 2000.
Lufthansa Chief Executive Carsten Spohr said it would be a "dark day" for the airline if the crash were confirmed.
"We do not yet know what has happened to flight 4U 9525. My deepest sympathy goes to the families and friends of our passengers and crew," Lufthansa said on Twitter, citing Spohr.
"If our fears are confirmed, this is a dark day for Lufthansa. We hope to find survivors," it said.
A spokesman for France's DGAC aviation authority said the airliner crashed near the town of Barcelonnette about 100 km (65 miles) north of the French Riviera city of Nice.
French accident investigators were heading for the crash site in Meolans-Revel, a remote and sparsely inhabited commune in the foothills of the French Alps.
Airbus said it was aware of reports about the crash.
"We are aware of the media reports," Airbus said on Twitter. "All efforts are now going towards assessing the situation. We will provide further information as soon as available."
Officials at Barcelona airport said the flight took off at 0855 GMT.
The crashed A320 is 24 years old and has been with the parent Lufthansa group since 1991, according to online database airfleets.net