Hospitals in Paris could have up to 90% of intensive care beds taken up with Covid-19 patients as soon as next week.
The warning came as France braces for new measures to slow a surge in cases.
"It's inevitable," Martin Hirsch, the head of the 39 hospitals in Paris and its suburbs, told the Parisien newspaper.
"By around 24 October, there will be a minimum of 800 to 1,000 Covid patients in intensive care, representing 70 to 90 percent of our current capacity," he said.
The prospect puts more pressure on President Emmanuel Macron, who is widely expected to announce tighter restrictions in a prime-time TV interview on Wednesday night.
He met with top ministers today to evaluate potential measures for slowing a second wave of infections.
In his last major TV interview, to mark the Bastille Day holiday in July, President Macron ordered that face masks be used in all enclosed public spaces nationwide. Since then, they have also become compulsory on the streets of Paris.
Media reports have speculated that new measures could include curfews in Paris and other cities placed on maximum alert because of fast-rising Covid cases that are again straining hospitals.
'Reduce social contacts'
On Saturday, the number of new infections rose by 26,896 in 24 hours - which was a record.
"Individual responsibility is 50 percent of this. We won't succeed if people don't get serious," a government source said.
Asked what he would like to see, Hirsch called for tighter work-from-home requirements and new measures to ensure social distancing.
In Paris and other at-risk cities, bars have already been closed, access to gyms has been sharply curtailed, and stricter crowd limits set on shopping malls and other venues.
The national health agency reported 94 Covid deaths in the previous 24 hours on Monday, and 171 new patients in intensive care.
Overall, 1,539 people are now in intensive care across France, which has a total capacity of some 5,000 beds. At the height of the crisis last April, more than 7,000 patients were in intensive care, some in emergency military field hospitals.
An expert panel set up to evaluate France's response to the pandemic reported on Tuesday that it found "clear failures of anticipation, preparation and management".
The panel, lead by Swiss infectious disease specialist Didier Pittet, was announced by President Macron last June.
Its conclusions are not due until December, but the "main findings" are being published "to provide advice that could be useful now," Pittet said at a press conference in Paris.
The experts pointed to a shortage of face masks early in the outbreak, when officials realised that emergency stocks had been allowed to dwindle in recent years.
Authorities were also slow to ramp up Covid testing, in part because unlike Germany, "France doesn't usually involve private labs in its strategy" but relies almost solely on hospitals, said Pierre Parneix, a panel doctor based in Bordeaux.
The report also noted a lack of coordination between various authorities and health agencies.
But it lauded "the exceptional adaptability and mobilisation" of health workers, which allowed the country's hospital system to "withstand the shock" as cases soared last spring.