A study by scientists at INSERM, the National Institute of Health and Medical Research, determined that 14,802 people had died in August.
The toll exceeds the prior government count of 11,435, a figure that was based only on deaths in the first two weeks of the month.
The country's largest undertaker had said earlier this month it thought the death toll was closer to 15,000 than the government was admitting.
The government's new estimate includes deaths from the second half of August, after the record-breaking temperatures of the first half of the month had abated.
The bulk of the victims — many of them elderly — died during the height of the heat wave, which brought suffocating temperatures of up to 104 degrees in a country where air conditioning is rare. Others apparently were greatly weakened during the peak temperatures but did not die until days later.
The new estimate comes a day after the French Parliament released a harshly worded report blaming the deaths on a complex health system, widespread failure among agencies and health services to coordinate efforts, and chronically insufficient care for the elderly.
Two INSERM researchers who delivered the report were to continue their analysis of deaths to determine what the actual cause was for the spike in mortality, the Health Ministry said.
The researchers were also to recommend ways of improving France's warnings system to better manage such heat-related crises in the future.
Earlier this month, the government commission recommended better coordination between health bodies in the future, reports CBS News Correspondent Elaine Cobbe, saying thousands of lives could have been saved if the alarm had been raised sooner.
But most of the top health officials were on vacation, and the government report says that also partly explains why the alarm wasn't raised sooner.
Local authorities in Paris are now reviewing plans for more home visits for the elderly during holiday and vacation times, reports Cobbe.
The heat wave swept across much of Europe, but the death toll was far higher in France than in any other country.
Health Minister Jean-Francois Mattei has ordered a separate special study this month to look into a possible link with vacation schedules after doctors strongly denied allegations their absence put the elderly in danger. The heat wave hit during the August vacation period, when doctors, hospital staff and many others take leave. The results of that study are expected in November.
The role of vacations is a touchy subject. The National General Practitioners Union says that only about 20 percent of general practitioners were away during the heat wave.
Other European countries hit by the heat have been slower than France to come out with death tolls, but it's clear they also suffered thousands of deaths.
Environmental experts warn that because of climate change, such heat waves are expected to increase in number in coming years, meaning Europe — a continent that historically has enjoyed a temperate climate — will have to make adjustments.