The current outbreak began in the Bordeaux region last November and since then 913 cases have been registered, said the national health authority (DGS), with more than 500 of them in the last month alone.
The departments of the Gironde and Vienne have seen the greatest numbers of measles cases, with the south west particularly badly hit.
A 32-year-old woman died last month in a hospital in the town of Poitiers from the disease, which causes skin rash and flu-like symptoms and can affect people of all ages, despite being considered primarily a childhood illness.
Only 519 cases of measles were registered for the whole of 2017.
The current trend “makes us fear an epidemic of considerable importance such as the one we observed in France between 2008 and 2012,” DGS director Jérôme Salomon told reporters.
Around 24,000 cases were registered in that outbreak, according to official figures.
The numbers then dropped spectacularly, with less than 400 cases a year between 2013 and 2015.
“The elimination of measles is a top priority for the World Health Organisation… To achieve that it is necessary to reach the goal of vaccinating 95 percent of people at risk,” said Salomon.
In France no department in the country has reached the 95 percent vaccination rate, health authorities say.
According to doctors the problem is that many in France – potentially up to one million – did not receive the necessary second injection of the MMR vaccination (Measles Mumps and Rubella).
“This second dose is necessary for the elimination of the disease because between 7% and 8% of children do not react to the administration of the first vaccine,” the doctor Daniel Lévy-Bruhl told Le Monde newspaper.
The people at greatest risk in France are those born after 1980, the year in which cases of the disease dropped dramatically, officials said. Most of this group have probably already had the measles, which used to afflict hundreds of thousands of children each year in France, and are now immune.
After the 32-year-old woman died in hospital in Poitiers hospital chiefs enforced a rule that all members of the public entering the emergency wards must wear a mask. Some 54 members of staff have had to be vaccinated.
Authorities are worried that the rate of vaccinations in the south western Nouvelle-Acquitane region is too low to cope with the epidemic.
It is believed between 70 and 81 percent of the public are vaccinated in the region.
Measles has been officially wiped out in the United States due to a vaccination programme put in place over recent decades.
France’s plans to eliminate the disease include making anti-measles injections one of the eight new vaccinations that became obligatory for all children born since January 1 this year.