The Grand Est region was the first in France to be overwhelmed by a wave of infections that has rapidly moved west to engulf the greater Paris region, where hospitals are desperately adding intensive care beds to cope with the influx.

The number of coronavirus deaths since March 1 climbed by 16 per cent to 3024, while the number of intensive care cases rose more than 10 per cent to 5107, rising after two days of falls.

Prime Minister Edouard Philippe has warned the country's 67 million people the toughest weeks in the fight against epidemic are still to come and doctors in the capital say they are close to saturation point.

"Today in the pulmonology unit we are as full as full can be," Jerome Pinot, a doctor at the Georges Pompidou hospital in Paris, told Reuters.

"To find a place in intensive care is a never-ending headache. We ask ourselves whether we can move this patient to this unit to take another patient. It's an incessant game."

France has increased the number of beds in intensive care units from 5000 to about 10,000 since the start of the crisis and it is scrambling to reach 14,500.

In the eastern city of Strasbourg, paramedics in hazmat suits transferred six patients onto three helicopters to move them to hospitals in Bern and Frankfurt.

Eighty have so far been moved from the region to Switzerland, Germany and Luxembourg. Transfers from Paris hospitals are expected in the coming days.

Health officials believe the benefits of a country-wide lockdown that has been in place since March 17 will begin to be felt by the end of the week.

They consider new daily hospital admissions and the number of those going into life-support as the key indicators to see if the tide is turning and if the health system can cope.

"We are not in a drop at the moment. We hope that this increase will be more modest in the coming days," Jerome Salomon, head of the French public health authority, told reporters.

Australian Associated Press