Huan Huan, on loan to Beauval zoo in central France from China, delivered the first cub at 10:18pm and the second at 10:32.
But soon after birth, the first, which weighed just 121 grams, began having problems breathing and died despite the best efforts of zoo staff.
"It was too weak to survive. The Chinese experts, who have experience of this, saw it straight away," zoo director Rodolphe Delord said.
"Our veterinary teams did everything they could to save it, but it was too small, too weak."
But he said the second twin, which weighed in at a healthier 142.4 grams, was in "perfect health".
The youngster has been put in an incubator so vets can give first-time mum Huan Huan a helping hand, zoo officials said.
The second of the two panda cubs is fed for the first time. Photo: AFP
Nine-year-old Huan Huan and her male partner Yuan Zi arrived at Beauval zoo in January 2012 on a 10-year loan from China after intense, high-level negotiations between Paris and Beijing -- was carrying a single cub.
Breeding pandas is notoriously difficult and this is the first time a cub has been born in France.
The female panda is only in heat once a year for about 48 hours. The gestation period for pandas is a mere 50 days.
Huan Huan (meaning "happy") and Yuan Zi ("chubby") are the only giant pandas living in France.
The pair were brought together in February, in the hope they would mate, but it didn't happen. In the end, the zoo performed an artificial insemination.
If all goes well with the birth, the surviving cub will leave Beauval in the next two to three years to be returned to China.