The 76-year-old man, who has not been named, died 75 days after the operation in Paris.
The bioprosthetic device, made by French company Carmat, is designed to replace the real heart for up to five years.
It is intended to help patients who are in the advanced stages of heart failure.
At this late stage of the disease, the damaged organ can no longer pump enough blood for the body to function normally.
When the device was fitted, the patient was said to have only a few weeks, or even days to live.
It’s not known whether his death was due to any malfunction of the artificial heart or the patient’s severe ill-health.
Three more patients in France with terminal heart failure are scheduled to be fitted with the artificial heart.
The clinical trial will be considered a success if they survive for at least a month.
A further trial of another 20 patients will examine to what extent the device improves their quality of life.
Eventually the company hopes to get a European license for the prototype heart, which is expected to cost around $240,000.
The Carmat device weighs nearly 2 pounds, three times that of a human heart. It is powered by an external lithium battery pack, which the patient wears on a belt.
It is made from a combination of synthetic materials, surrounded by a plastic shell.
Inside the heart, some of the surfaces which come into contact with blood are made from cow heart tissue, which are less likely to cause clots to form.
The patient trials follow many years of laboratory research and extensive animal studies.
The Carmat heart is designed to work for five years.
Artificial hearts have been used for decades, but usually as a means of helping a failing heart to pump blood around the body.
Several companies are working on devices which entirely take over from the damaged organ until a donor heart becomes available.
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