Almost 300 COVID-19 patients are in the main hospital in Papeete, with many others being cared for at home because there are no beds left.
Although France and New Caledonia sent some personnel, the hospital says it needs reinforcements as infection rates remain high.
In a post, the hospital reminded Mr Macron of his visit to the hospital in last month when he said they were all part of France and they would all be protected.
The French Polynesian president Edouard Fritch has meanwhile called on the public across the territory to observe September 5th with a fast to remember those who died of the pandemic that has spread to 45 islands.
Vaccinations have been continuing and almost half the population has had one jab.
While many organisations accept a new law making COVID-19 vaccinations compulsory for people in contact with the public, others have reservations.
The police union said it expects its members to get vaccinated while hospital staff unions say they were awaiting the outcome of a challenge of the law in Paris.
The port workers' union said it is for vaccinations but against them being compulsory, adding its members could strike and block the port.