Another man, who shared a hospital room with him for three days, was later found to have the nCoV-EMC virus, which is a cousin of the Severe Acute Respiratory Syndrome (SARS) that sparked a health scare around the world in 2003.
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 WHO 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.