Of these 38, 12 patients have now returned to health; two have died; and 24 continue to remain in hospital in quarantine - with two of these in a serious condition.
Mr Véran said: “Tonight, we are seeing a significant increase in the number of cases in our country.”
Who are the new cases?
The majority of them - 12 - have been diagnosed in the Oise department (Hauts-de-France). Three more cases were on a military base.
Some - three members of the same family, plus a family friend - were diagnosed in Annecy (Haute-Savoie, Auvergne-Rhône-Alpes).
How did they become ill?
The 12 cases in the Oise appear to have all been infected by the same person; a 60-year-old teacher who had the virus, and who died overnight between February 25-26. This also applies to the three people on the military base. Investigations are ongoing to confirm this.
Mr Véran said: “These seem to be linked by a chain of contamination.”
As for the family in Annecy, it appears that one man and his wife had recently returned from Lombardy, the area in northern Italy that has seen the biggest outbreak of the virus in Europe. Their daughter, and a friend of the couple, have become the latest cases, and appear to have caught the virus from the couple.
What has been done to help?
Investigations are ongoing into the chain of contamination, to see if there are any other cases connected to these latest diagnoses, Mr Véran said.
He added: “We are at the stage of slowing [and] limiting the spread of the virus across our country. A team is meeting tomorrow, including infection specialists, emergency doctors, hygienists and epidemiologists, to strengthen all the necessary investigations.”
The diagnosed patients have been hospitalised - including in hospital in Compiègne (Oise) - and will be kept in quarantine in hospital for 14 days, regardless of their condition. Other patients have been taken to the CHU in Amiens (Somme), and a hospital in Creil (Oise).
At the hospitals themselves, precautions are being taken among staff.
In Creil - the hospital that had been taking care of the 60-year-old man who died - the emergency department has closed, and staff who had been in contact with him are staying at home, isolating themselves.
Nurses and doctors still working on-site are wearing masks.
The French government has also set up a free telephone number that the public can call, seven days a week, 24 hours a day, for information and updates on the virus.
What is their current condition?
The condition of all of the newly-diagnosed patients has not been revealed. But so far, Mr Véran has said that the young girl and friend of the Annecy couple, at least, are “not in a worrying state”.
Two patients are in a serious condition, it has been reported.
Is there any risk?
The confirmed patients are now in quarantine, and investigations are continuing to see if the “chain of contamination” could have affected anyone else. In the Oise, the investigation is seeking to confirm the so-called “patient zero” - the initial source of the outbreak.
It is not clear yet if anyone else has been at risk.
Across France, around 2,000 school pupils have not gone back to school in areas affected by the virus, education minister Jean-Michel Blanquer said. They are being asked to stay at home.
He said: “This number will rise next week, when a second third are expected to come back from holidays, and we will have updated our evaluation on the development of the illness.”
The director general of the World Health Organisation (WHO), Tedros Adhanom Ghebreyesus, recently said that the world “is at a decisive point”. He said: “No country should assume it won’t get cases; that could be a fatal mistake, quite literally. This virus does not respect borders.”
The health advice to avoid the spread of the virus remains the same: wash hands regularly, use hand sanitizer gel to clean hands and any high-traffic areas or devices, and cover your mouth with the crease of your elbow (rather than your hand) if you are coughing. Avoid people who are ill.
if you have travelled to an at-risk area - such as China or northern Italy - isolate yourself for 14 days even if you have no symptoms, and stay alert to any developing signs.
Wearing a mask may help you to avoid infecting others, if you are ill.
