This is out of a total of 29.2 million calls made to 101 centres across France.
The worrying investigation, carried out by Le Point using the health services' own database of statistics for 2016, ranked the emergency medical service centres according to how effectively they respond to calls.
And it showed that the rate of emergency calls that go unanswered in Paris is particularly high, with just over 50 percent of calls not followed up.
Similarly, in Perpignan near the Mediterranean coast, just over 42 percent of calls were not followed up.
The situation was also revealed as particularly bad in the French overseas territories, with 57 percent of calls not picked up in Pointe-à-Pitre, Guadeloupe, and 37.39 percent in Fort-de-France. France, Martinique.
Only two call centres across France, in Orleans and Verdun met the goal of answering calls within a minute, which should be standard practice.
According to the report, in Paris just 36 percent of calls were handled within a minute, making the the SAMU centre in the French capital one of the worst.
The news puts an uncomfortable spotlight on SAMU just a few months after the public outcry over the death of a young woman from Strasbourg when her distress call to emergency services was mocked by the operator.
However the president of Samu disputed on Thursday the results of the report.
“I believe that Samu is not exemplary in its operation, but what must be said is that it is not 4.6 million patients who have been unable to contact the service” François Braun told the French press.
“There are not – and we are absolutely certain of it – 4.6 million patients who cannot reach Samu, imagine for a moment that this is true, it would be a health scandal that wouldn't have taken years to be revealed,” he said.