"It cannot be accepted that the IOC is not listening to the number one Olympic sport," Andre Giraud said. "Everyone agrees that the Games cannot be held on the dates planned."
The US and Spanish athletics federations have also asked for a postponement. Sebastian Coe, the head of World Athletics, has also hinted that such a step may be inevitable.
The French Health Minister Olivier Veran also said Sunday he was reluctant to send athletes to Japan for the Games.
"Do I have the right to ask for the suspension of the Olympic Games as Minister of Health? No," he said.
"Do I see myself sending athletes to Japan today or asking them to prepare themselves in good conditions? The answer is no."
Giraud told AFP that the IOC should already be thinking of what he called "Plan C", a postponement to 2021, joining a swelling chorus of objections to holding the Games this summer.
"If the crisis is contained by the end of May, we can envisage a postponement of the Games to the autumn. But Plan C would be a six-month or one-year postponement," he said.
"How can we bring together 11,000 athletes in less than four months in the Olympic village? The athletes are in a stressful situation and we need to reassure them. We can't wait any longer.
Giraud also urged the French National Olympic Committee (CNOSF) to "take a stand".
"I appeal to the CNOSF to take action with the IOC. We need a national position of solidarity," he said.
"At the Games, the French team is under the CNOSF banner. The responsibility at national level therefore lies with the CNOSF President to listen to his federations and take a stand."
IOC president Thomas Bach has signalled his determination to press ahead with the Games in Tokyo from July 29 to August 9, telling the New York Times that postponement "would not be responsible now" as "we are four-and-a-half months away from the Games".
On Friday, USA Swimming said they wanted the Games postponed. They were soon joined by France's swimming federation, the US and Spanish athletics federations, the Norwegian Olympic Committee as well as likely competitors.
"I don't think we should have the Olympic Games at all costs," said Coe, who ran the 2012 London Games. "A decision on the Olympic Games may become very obvious very quickly."
On Sunday, American daily USA Today reported that there was wide support from US athletes for the postponement of the Games.
It reported that almost three-quarters of the 300 US athletes who took part in a virtual town hall with US Olympic officials support a delay.