Summit Explorers co-owner Mr Vialletet died with a client on Monday night while climbing in a four-person team.
The climbers were roped together in pairs and climbing from Empress Hut to the summit when two fell from the mountain's west ridge.
A givealittle page has been set up to provide emergency support for Mr Vialletet's family.
The page describes him as "a loving father, husband, and integral part of the Wānaka and New Zealand guiding whānau".
"Our hearts are focused on the family he cherished. Thomas leaves behind his loving partner, Danielle, and their two beautiful young children.
"Through his guidance, kindness, and professionalism, Thomas profoundly touched the lives of countless clients, mentees, and friends."
Mr Vialletet was the core provider for the family, and their financial security was dependent on the income generated by their small guiding business, the page said.
"His sudden loss means Danielle and the children face the immediate challenge of losing their main source of income, compounding their immense grief."
Wānaka-based Adventure Consultants chief executive Guy Cotter told Allied Media that Mr Vialletet was a wonderful person and his absence would be felt throughout the community.
‘‘I am really devastated by what occurred, it’s a very trying time for everyone who knew him - especially his family,’’ he said.
Mr Vialletet's business profile says he grew up in the French Alps where he had been climbing, skiing and exploring mountains for over two decades.
"His quest for mountain adventures brought him to New Zealand and he immediately fell in love with the wilderness of this country."
Mr Vialletet was a climbing instructor before becoming a full IFMGA Mountain and Ski Guide and was also part of the French National Young Alpinism Team between 2009 and 2012.
NZMGA president Anna Keeling said he was a member of their organisation, was "careful and diligent", and had been guiding for at least 12 years.
He last climbed Mt Cook just two weeks ago, "via the quite difficult East Ridge".
"He was very qualified to be up there and knew the route well and knew the conditions well this year. So it's very shocking."
Head torches used to find survivors
The head torches from the two survivors of the ill-fated climbing trip helped guide a Dunedin helicopter rescue team to their location in the middle of the night so they could be flown to safety.
The team was called to Aoraki/Mt Cook on Monday night.
Helicopters Otago pilot Andy Craig, of Dunedin, said they located the two climbers near the summit using night-vision goggles.
They saw the bright light from their headlamps and were able to pinpoint their exact location.
"You can see any light for miles away with the night vision goggles, so it was pretty quick to locate the two."
After winching them to safety at 2.15am, Mr Craig headed to the Department of Conservation rescue headquarters in Mt Cook Village.
The New Zealand Mountain Guides Association (NZMGA) said the party - two guides and two clients - were completing a grand traverse of the mountain.
"One climber was seen sliding off the ridge, down the western side of Aoraki and then pulled the second climber, who was attached by a rope, off that same side," Search and Rescue pilot Nigel Gee told 1News.
"They both slipped and went possibly about a 1500-foot [460m] slide."
Their bodies were found about 4.30am and had since been recovered with Doc’s help.
Canterbury Aoraki area commander Inspector Vicki Walker said police were in the process of contacting the next of kin.
"Until that process has been completed we won't be releasing any further information."
"NZMGA’s focus is now on those most affected and our priority is supporting the family, including their partner and children, as well as our wider guiding community during this extremely difficult time."
Police said they were made aware of the incident on the mountain about 11.20pm.
Two helicopters were sent. One from Queenstown flew to Wānaka and picked up the Aoraki Doc search and rescue team, while the one from Dunedin flew directly to the mountain and began searching.
Alpine cliff rescue specialists were on board.
Aoraki/Mt Cook is New Zealand's highest peak at 3724m.
