"The first patient is dead," an official said, referring to the man who was hospitalised on April 23.
Last month it was a revealed that the man was hospitalized in Douai, northern France after returning from a holiday in Dubai. He was being treated in isolation, where up until Tuesday his condition was described a "very serious but stable condition".
French Health Minister Marisol Touraine expressed sadness over the death, adding: "Authorities remain on alert but ... there is no new situation in our country regarding the epidemic."
It was then revealed that another patient who had shared a hospital room with the 65-year-old victim had been diagnosed with the virus.
The other man, who is in his 50s, has been in hospital in the northern city of Lille since May 9.
The new virus has killed 19 people. Like SARS, it appears to cause an infection deep in the lungs, with patients suffering from a temperature, cough and breathing difficulty, but it differs from SARS in that it also causes rapid kidney failure.
There have been 44 laboratory confirmed cases worldwide of the virus, which until now has been known as the novel coronavirus, or nCoV-EMC, but was redubbed the Middle East Respiratory Syndrome Coronavirus, or MERS.
Saudi Arabia counts by far the most cases, with 30 confirmed infections and 17 fatalities, while cases have also been detected in Jordan, Qatar, Tunisia, the United Arab Emirates, Germany, Britain and France.
Scientists at the Erasmus medical centre in Rotterdam have determined that the virus appears to infect the body via a docking point in lung cells, suggesting bats may be a natural reservoir for it.
Bats were also pinpointed as a likely natural reservoir for SARS in a 2005 study, and are known carriers of the deadly haemorrhagic fever Ebola.
The World Health Organization said Friday that much uncertainty remained surrounding MERS, stressing that it aimed to work closely with Saudi Arabia, Tunisia and perhaps other Middle Eastern countries to determine how great the risk is.
While the virus has been deadliest in Saudi Arabia, cases have also been reported in Jordan, Germany, Britain and France.
But speaking earlier in May, WHO spokesman Gregory Hartl told AFP there they saw no reason to change its travel recommendations because of the new virus.
"We have not seen general transmission in the community, again we have only seen transmission among very, very close contacts," he said.
"So from that point of view the risk is very small and there is no reason yet to make any changes to our recommendations".