Thousands of people, most of them elderly, have been admitted to hospital due to an outbreak of a virulent strain of the virus known as H3N2.
Last week 395 in every 100,000 French people consulted their doctor over flu symptoms, up from 326 the previous week, health authorities report.
But the number of people going to emergency services and the number of hospitalisations fell slightly last week, to 4,788 and 787 respectively.
Touraine called on the country’s hospitals to delay non-urgent operations to make room for those affected.
“We are approaching the peak of the epidemic, which means that we are in the middle of it," she said on Wednesday. "People will continue to fall ill. So I am asking all hospitals, private and public, to see if it is possible to postpone certain appointments, including surgery, in order to free up beds for flu patients.”
Elderly worst hit
The virus is most likely to affect people over the age of 65.
Most of the people admitted to hospital were over 80 and were kept in for 10-15 days.
Of France's 850 hospitals, 142 have declared themselves to be under pressure, allowing them to add beds, recall healthworkers on holiday or cancel non-urgent operations.
Some doctors have criticised the closure of beds over the last 20 years, claiming it has left hospitals underequipped to face the annual flu outbreak.
This year's outbreak started earlier than usual, in December and 784,000 people have seen a doctor for symptoms since then.
In 2014-15 nearly 2.9 million people were hit by an epidemic that caused an estimated 18,300 extra deaths, most of them of people over 65.