The patients suspected of having contracted the virus are both men who have recently spent time in Saudi Arabia and they have been hospitalised in Tours, a town in the Loire region south of Paris.
France has had two confirmed cases of MERS to date, including one which led to a death in the northern town of Lille last month.
In its most recent update on the virus, the World Health Organisation (WHO) said on June 7 that there had been 55 laboratory-confirmed cases of the virus, 31 of which had resulted in the affected individuals dying.
Previously known as novel coronavirus, the disease was last month renamed Middle East Respiratory Syndrome Coronavirus, or MERS-CoV.
The WHO believes 26 of the 31 people who have died contracted the virus in Saudi Arabia.
The virus is a cousin of Severe Acute Respiratory Syndrome (SARS), which sparked a global scare in 2003 after jumping to humans from animals in Asia and claiming 800 lives.
Like SARS, MERS appears to cause a lung infection, with patients suffering from a temperature, cough and breathing difficulty.
But it differs in that it also causes rapid kidney failure and the extremely high death rate has caused serious concern among health experts.