The updated estimate included deaths in the second half of August after record-breaking temperatures had abated, said Isabelle Dubois-Costes, a spokeswoman for General Funeral Services.
While the bulk of the victims — many of them elderly — died during the heat wave, others apparently were greatly weakened during the peak temperatures but did not die until days later.
The latest estimate came after the government on Monday released a report blaming the deaths on hospital understaffing, bureaucratic delays and insufficient care for the elderly.
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.
The government late last month released an official estimate of 11,435, but the Health Surveillance Institute said on Tuesday that those numbers were based on deaths only in the first half of August.
The institute said it would release an estimate of deaths for all of August at the end of September.
General Funeral Services has 25 percent of the funeral market in France, and compiled its tally by estimating the increased number of deaths it handled in August compared to last year, then multiplying the result by four to get an estimate for the whole country.
The company was the first to come forward with a death estimate that registered the magnitude of the disaster when it announced in August that some 10,000 had died. The government at that time had put the figure at 3,000 at the most.
The new figures could put even more pressure on the government to correct snags in its highly respected health system and increase outrage over the staggering death toll.
The heat wave brought suffocating temperatures of up to 104 in the first two weeks of August in a country where air conditioning is rare. The heat baked many parts of Europe, killing livestock and fanning forest fires.
The high death toll has triggered an angry debate in France over shortcomings of the health system. The government is considering eliminating a national holiday to raise revenues for elderly care.
The French lifestyle has also come under scrutiny, since some of the elderly victims died alone in their homes while families were away on lengthy August holidays. Authorities reportedly had difficulties making contact with survivors who were away on vacation.
French doctors on Tuesday reacted angrily to the government report.
Gilles Brucker, director of the Health Surveillance Institute, disputed the report's assertion that the institute failed to perform as it was supposed to as temperatures rose dangerously high.
The institute "did all that it was asked," Brucker was quoted as saying in an interview published Tuesday in Le Parisien newspaper. He added that he would not resign because his organization committed "no major faults."
Brucker also disputed the report's allegation that an alert system would have made a substantial difference in the scope of the disaster.
"I can tell you that even if the (Institute) had raised the alarm with all its might, it wouldn't have changed much," Brucker said. "To sum up the causes of this tragedy to the lack of an alert is unacceptable."
He said France simply needs a heat wave plan "because the entire country wasn't prepared for such a catastrophe."
The institute surveys numerous diseases and other maladies, but "the heat wave was never our mission," Le Parisien quoted him as saying.