Macron is the first foreign head of state to visit the vast territory -- located at the crossroads of the Atlantic and the Arctic -- since Trump's annexation threats.
Trump, since returning to the White House in January, has repeatedly said America needs the strategically located, resource-rich island for security reasons, and has refused to rule out the use of force to secure it.
Denmark has also repeatedly stressed that Greenland "is not for sale."
Macron said his visit was aimed at conveying "France's and the European Union's solidarity" for "the sovereignty and territorial integrity" of Greenland.
Danish Prime Minister Mette Frederiksen, Greenlandic Prime Minister Jens-Frederik Nielsen, and dozens of Greenlanders waving their territory's red-and-white flags, were on hand to greet the French president.
Macron kicked off his six-hour visit with talks on board a Danish frigate with Frederiksen and Nielsen.
He was to later visit a glacier to see firsthand the effects of global warming. A visit to a hydroelectric plant was initially scheduled but was cancelled at the last minute.
Macron's trip to Greenland was "a signal in itself, made at the request of Danish and Greenlandic authorities", his office said ahead of the trip.
- 'Not for sale' -
The Danish invitation to Macron contrasts sharply with the reception granted to US Vice President JD Vance, whose one-day trip to Greenland in March was seen as a provocation by both Nuuk and Copenhagen.
During his visit to the US Pituffik military base, Vance castigated Denmark for not having "done a good job by the people of Greenland", alleging they had neglected security.
The Pituffik base is an essential part of Washington's missile defence infrastructure, its location putting it on the shortest route for missiles fired from Russia at the United States.
Polls indicate that the vast majority of Greenland's 57,000 inhabitants want to become independent from Denmark -- but do not wish to become part of the United States.
Unlike Denmark, Greenland is not part of the European Union but is on the list of Overseas Territories associated with the bloc.
The Arctic has gained geostrategic importance as the race for rare earths heats up and as melting ice caused by global warming opens up new shipping routes.
Copenhagen in January announced a $2 billion plan to boost its military presence in the Arctic region.
NATO also plans to set up a Combined Air Operations Centre (CAOC) in Norway above the Arctic Circle, as Russia aims to bolster its military presence in the region.
During his visit, Macron plans to discuss Arctic security and how to include the territory in "European action" to contribute to its development, while "respecting its sovereignty", his office said.
- Mount Nunatarsuaq -
Macron scheduled glacier visit was to Mount Nunatarsuaq, about 30 kilometres (19 miles) from Nuuk, to see firsthand the effects of global warming on the frontlines in the Arctic.
The Arctic is warming four times faster than the rest of the planet, according to a 2022 study in scientific journal Nature, and Greenland's ice sheet melted 17 times faster than the historical average during a May 15-21 heatwave, a recent report showed.
France intends to "massively reinvest in the knowledge of these ecosystems," following in the footsteps of famed French explorer Paul-Emile Victor who carried out multiple expeditions to Greenland, Macron's office said.
Greenlandic authorities recently designated Victor's hut, built in 1950 in Quervain Bay in the north, as a historic structure.
