The outbreak has now reached 11 total reported cases, nine of which have been confirmed.
Three people on the cruise died, including a Dutch couple that health officials believe were the first exposed to the virus while visiting South America.
The French passenger hospitalised in Paris has a severe form of the disease that has caused life-threatening lung and heart problems, said Dr. Xavier Lescure, an infectious disease specialist at Bichat Hospital.
He said the woman is on a life-support device that pumps blood through an artificial lung, providing it with oxygen and returning it to the body. The hope is that the device relieves enough pressure on the lungs and heart to give them some time to recover. Lescure called it "the final stage of supportive care."
With the evacuation of all passengers and many crew members complete, the MV Hondius is now sailing back to the Netherlands, where it will be cleaned and disinfected.
The director of the World Health Organization said confirmed and suspected cases have only been reported among the cruise ship's passengers or crew.
"At the moment, there is no sign that we are seeing the start of a larger outbreak," said Tedros Adhanom Ghebreyesus, the WHO director general.
"But of course the situation could change, and given the long incubation period of the virus, it's possible we might see more cases in the coming weeks."
The latest person confirmed to be infected is a Spanish passenger who tested positive for hantavirus after being evacuated from the ship, Spain's health ministry said Tuesday. The passenger was in quarantine at a military hospital in Madrid.
Health authorities say it's the first hantavirus outbreak on a cruise ship. While there is no cure or vaccine for hantavirus, the WHO says early detection and treatment improves survival rates.
Argentina's health ministry said Tuesday a team of scientific experts will be dispatched in the coming days to investigate the origin of outbreak.
A Dutch couple, identified by the WHO as the first cruise passengers infected with hantavirus, spent several months in Argentina and neighbouring South American countries before boarding the cruise ship. The husband and wife later died.
Argentine officials have said the couple took a bird-watching tour that included a stop at a garbage dump where they may have been exposed to rodents carrying the infection.
The health ministry said its team will investigate the landfill and other locations the couple visited where rats known to carry the virus are found.
A total of 87 passengers and 35 crew were escorted from the ship to shore in Tenerife by personnel in full-body protective gear and breathing masks in a carefully choreographed effort that ended on Monday night.
Two aircraft arrived in the southern Dutch city of Eindhoven overnight carrying Dutch nationals as well as passengers from Australia and New Zealand and crew members from the Philippines. All were placed into quarantine, according to the Dutch government.
Hantavirus usually spreads from rodent droppings and is not easily transmitted between people. But the Andes virus detected in the cruise ship outbreak may be able to spread between people in rare cases. Symptoms - which can include fever, chills and muscle aches - usually show between one and eight weeks after exposure.
WHO chief Tedros has advised that returning passengers should stay in quarantine, either in their homes or in other facilities, for 42 days.
Twelve employees at a Dutch hospital where a passenger from the Hondius is being treated have to quarantine for six weeks after improperly handling bodily fluids, Radboud University Medical Center said in a statement Monday night.
The "risk of infection is low" the hospital said, but was requiring the dozen employees to go into preventive quarantine as a "precaution."
The hospital in the eastern city of Nijmegen received a passenger last week from one of the evacuation flights that landed in the Netherlands and the person has since tested positive for hantavirus.
