The royal family declared a month of mourning, as flags were lowered to half-mast nationwide Wednesday. Danish daily Politiken headlined "Au Revoir, Henrik" above a photo of the dashing young prince waving from a convertible.
Diagnosed with dementia in September 2017 and hospitalised since January 28 for a lung infection, Henrik passed away late Tuesday.
A private funeral will be held on February 20 at the Christiansborg Palace chapel in the capital, the palace said.
Prior to that, Danes will be able to pay their respects at the chapel, where the princes closed casket will be on display for three days.
In line with his wishes, he will be cremated. Half of his ashes will be spread in Danish waters and half buried on the grounds of Fredensborg Castle north of Copenhagen.
Danish Prime Minister Lars Lokke Rasmussen said the prince had "represented Denmark magnificently.
"His commitment was infectious, and his insight great."
French President Emmanuel Macron said Henrik had helped promote the "long and unfailing friendship between France and Denmark."
Outside Amalienborg, the royal's main residence in Copenhagen, Danes laid down flowers, children's drawings, and candles.
One of them, Nina Langebaek, told AFP she would remember the prince as interested "in art, poetry, and making food.
"He was a great ambassador for Denmark."
With a jovial face, the prince had a reputation as a bon vivant.
But frequent outbursts of anger and a flamboyant style in a country that values humility and discretion irritated some Danes.
Disappointed his royal title of prince was never changed to king when his wife became queen in 1972, Henrik voiced his frustration in the media, which did not endear him to subjects who found him arrogant.
He retired from public service in 2016, then announced he did not want to be buried next to his wife because he was never made her equal.
His decision broke with the tradition of burying royal spouses together in Roskilde Cathedral west of Copenhagen.
Born Henri Marie Jean Andre de Laborde de Monpezat on June 11, 1934 in Talence, near Bordeaux, Henrik spent much of his youth in Vietnam, then a part of Indochina, where his father was a businessman.
He met Margrethe -- then crown princess -- while stationed in London as a diplomat.
Upon marrying her, he changed his name to Henrik, converted from Catholicism to Protestantism and renounced his French citizenship to become a Dane.
Teased for his French accent and unable to understand why protocol required him to remain in his wife's shadow, Henrik never really found his place in Denmark.
It wasnt until 1997 that he stood in for his wife at a public engagement for the first time.
In 2002, he made headlines when he fled to his chateau in southern France to "reflect on life", complaining he didnt receive enough respect in Denmark after his son, Crown Prince Frederik, was chosen to represent the queen at a New Years ceremony instead of him.
He said he felt "pushed aside, degraded and humiliated."
Some politicians dubbed Henriks behaviour "tiresome", while media had a field day. One television show conferred on him the title of "Whiner of the Year".
But it also marked a turning point, as Danes saw a more vulnerable side of Henrik and slowly started to warm to him.
Over time, his contrarian streak and flamboyance helped earn him cult status among young people.
In 2013, he played piano with Danish pop group Michael Learns To Rock, on a track recorded for the king of Thailand.
Months later he was photographed strolling with friends in the self-governed Copenhagen hippie community of Christiania, known for its cannabis trade, and in June 2014 he dressed up in a panda costume at a charity event.
In April 2015 he controversially cancelled his appearance at Margrethe's 75th birthday celebrations for ill health, only to resurface in a tourist-packed square in Venice less than two days later.
The tabloids were outraged, but fans saw it as the kind of erratic behaviour they had come to love him for.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)