It is believed Darren Rodgers, who was 24 and from Ballymena, was on his own and fell about 26ft (8m) from a promenade onto a rocky beach in Nice.
Supt Nigel Goddard, who is leading the PSNI team in France, said he was told it was an accident and not in any way disorder related.
Tributes have been paid to Mr Rodgers by his friends, fellow fans, and by the Irish Football Association (IFA).
The accident happened in the early hours of Monday, shortly after Northern Ireland played its first match of the Euro 2016 finals against Poland in the city on Sunday night.
Mr Rodgers was from the Meadowvale area of the County Antrim town and was a former pupil of Cambridge House Grammar School.
In a statement, his family thanked the local community for their support.
Supt Goddard said: "I was informed this morning by my French counterparts of this tragic news
"I believe it was an accident."
Northern Ireland's first and deputy first ministers, Arlene Foster and Martin McGuinness, issued a joint statement.
"It was with great shock and sadness we learned this morning of the death of Darren Rodgers in Nice last night as the result of a tragic accident," they said.
"The loss of a young life in these circumstances is truly heartbreaking and our thoughts and prayers are with his friends and family at this extremely difficult time.
"This sad news is in stark contrast to the jovial carnival atmosphere just hours before at the game against Poland."
DUP North Antrim MLA Paul Frew said he had spoken to Mr Rodgers on Sunday.
He described him as a "great lad with a big heart".
"Darren played for Braid Utd. Would have ran through a brick wall for his mates. Whole team is in shock, simply can't believe it," Mr Frew tweeted.
Patrick Nelson, the chief executive, of the IFA said: "On behalf of the board, management, players and staff of the Irish Football Association, I would like to express my deep sadness at the tragic death of a Northern Ireland supporter in Nice in the early hours of this morning.
"The thoughts of everyone at the association are with his family and friends at this time."
Gary McAllister of the Amalgamation of Northern Ireland Supporters Clubs said: "I'm sure that every Northern Ireland fan, both here in France and at home, will be thinking of Darren and his loved ones at this very sad time."

Some machines were blown up using "powerful explosives", while others were dragged outside and attacked with high-powered saws to access the cash.
The seven men were convicted of conspiracy to cause an explosion and burglary at Liverpool Crown Court.
They are due to be sentenced on 19 April.
The gang, mostly from Merseyside, was caught after a covert police operation.
The court was told they carried out 13 raids between February 2015 and February 2016.
The attacks happened in Sonnings Common and Woodstock, Oxfordshire; Alsager and Culcheth, Cheshire;  Huyton, Merseyside; Hucclecote, Gloucestershire; Swindon, Wiltshire; Bury-St-Edmunds, Suffolk; as well as in Aberdeen, Carnoustie, and Perth.
An investigation by TITAN, the Northwest Regional Organised Crime Unit, found the gang stole high-powered vehicles to carry out the raids which they concealed in a special trailer attached to a lorry.
The men slept in hammocks inside the trailer which also had fuel containers to reduce the number of times they had to use petrol stations or motorway services, Merseyside Police said.
Det Ch Supt Chris Green, head of TITAN, said: "These individuals believed they were untouchable and they used dangerous tactics in targeting ATM's, which clearly put members of the public at risk."
Maria Corr, of the Crown Prosecution Service, added: "These men were ruthless, organised criminals who conspired to cause explosions and burgle banks up and down the country.
"They thought nothing of using powerful explosives to blow up cash machines in residential areas, putting nearby residents in real danger."
A Northern Ireland football fan has died in an accident in France.
[NEXT_CONCEPT]
A gang blew up cash machines at banks and supermarkets across England and Scotland stealing hundreds of thousands of pounds, a court has heard.