Local officials have said there is no hope of survivors from the crash.
But Mr Fyfe said rescue teams had found debris and pieces of the aircraft floating on the surface of the water which could indicate survivors may yet be in the sea.
Speaking to reporters at Air New Zealand's Auckland headquarters, he said Air New Zealand had been told officially that one body had been recovered from the crash site.
Mr Fyfe gave further details of the acceptance flight, which was a handover from German charter company XL Airways, which had leased the Airbus 320 from Air NZ for the last two years.
He said the plane had left Perpignan and flown for two hours as part of the test flight. It was captained by the two XL pilots as the plane was still on the German airlines' register.
"The role of our team was to observe the performance of the aircraft and to validate that it met Air NZ operating standards and the return policies requirements," he said.
"All of the ground checks on that aircraft had been completed. The maintenance had been completed and it was on an acceptance flight."
There was no indication yet of any Mayday calls or distress alerts to ground crew from the plane, which was returning to Perpignan when it crashed, he said.
A spokesman for XL Airways said: "At this point we do not know exactly what happened. At first we heard the plane had managed an emergency landing on water but then the coast guard said the plane had broken apart."
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Victims' families
Mr Fyfe said the Air New Zealand staff on board were a senior pilot, based in Auckland, two engineers based in Christchurch and an engineer from Auckland.
He described the Air NZ captain on board as "very experienced".
Support teams from Air New Zealand were with the families of the missing New Zealanders.
Mr Fyfe said he had not yet spoken to the families but would later today as more details came through on the rescue efforts.
He said he would fly to Perpignan this evening and has offered places to any family members who want to go there.
Air New Zealand deputy CEO Norm Thompson will fly to France on the first available flight, at midday.
"I think here at Air NZ it is a very tight-knit team and people are feeling a real deep concern at the moment. I have had endless calls from people offering support and wanting to do anything they can to assist," Mr Fyfe said.
"It's a very very difficult time when there is any possibility that some of our colleagues may have been hurt, injured or potentially killed. That creates a lot of emotion so it's really difficult."
The CAA inspector on board the flight was there to recertify the plane before it was returned to New Zealand.
Recertification of planes is normal practice when an aircraft has been used by another airline and is about to be registered in New Zealand.
Spokesman Bill Sommer said the CAA staff member was from Wellington. Staff were liaising with the inspector's family but couldn't comment further until they received confirmation from French authorities on the names of the people involved.
He expected a media conference would be held later today.
Mr Sommer said the CAA wouldn't be involved in the investigation but the Transport Accident Investigation Commission could be.
'No hope'
A French official earlier said there was no hope of finding survivors.
Dominique Alzeari, assistant prosecutor at Perpignan who is partly in charge of the investigation, told AFP there was "no hope of finding survivors".
He told French broadcaster TF1 the search would be called off at 11.30pm local time (11.30am NZT) and resume in the morning.
A spokesperson for the Marine Department in Toulon also told
Le Monde
newspaper: "There are no survivors."
In brief:
* Air NZ Airbus 320 crashes 4.30am NZT off French Coast
* Five New Zealanders among seven people on board
* At least one body recovered
* Flight heading from Perpignan for Frankfurt when attempted emergency landing
* A320 leased by German company XL for two years but being handed back to Air NZ
Do you have any information on the crash? Email nzherald.co.nz
The crash comes exactly 29 years after the Mt Erebus disaster, when Air NZ flight TE901 flew into Antarctica's highest mountain killing 257
Mr Fyfe said the anniversary added a new dimension to today's tragedy, which was already poignant for Air New Zealand staff.
"Naturally, this is an extremely difficult time for us all and the full resources of the airline are being put into investigation."
Skipper alerted authorities
Maritime affairs officer Nicolas Renaud told BFM television French authorities had been alerted to the accident by the skipper of a sailing boat who said he saw the plane go down.
"The plane appears to be in several pieces," he said.
TF1 in France said the plane was coming into land when it crashed approximately 5km offshore.
A member of the local government in Roussillon told France Info: "The plane, while coming into land at Canet-en-Roussillon, had started to turn and went straight into the sea."
Another witness told the radio station he saw the Airbus dive abruptly and plunge into the sea.
"I could see it was an airliner because I saw two large engines. There was no fire, nothing," the witness, a local policeman said.
"It was flying straight, then it turned brutally towards the ground. I said to myself it will never pull out and there was a big spray of water," he said.
A French journalist said it was unclear why the plane had crashed.
"It's not really clear on what happened...the plane was flying for one hour and a half and suddenly fell down to the sea," he told Radio New Zealand.
"There was no explosion, it was flying (at) 300m and suddenly fell down into the sea, but no explosion."
One witness who watched the accident happen from the coast told local newspaper
L'Independant
the plane "made an attempt to climb but fell back down again immediately".
"I saw an enormous splash of water then, a few seconds later, I heard the noise. It was terrifying."
The search
Debris from the plane was spread over hundreds of metres from the scene of the crash, the mayor's office in Canet-en-Roussillon said.
First Officer Sandrine Parro of the Regional Operational Centre for Monitoring and Rescue (CROSS) for the Mediterranean told AP five launches, two helicopters and a patrol plane had been dispatched to the area of the crash.
One hundred police and firefighters were in attendance.
"The fuselage has been located. The rescue operations will determine if there are any survivors," she added.
AFP said 20 specialist divers were involved in the search and that French navy ships were looking for the plane's black box - which records flight information.
Six French and two German aviation accident investigators were being sent to assist.
A minehunter was also being sent to the scene to help search for the aircraft's blackbox,
L'Independant
reported.
The French transport minister Dominique Bussereau would visit Perpignan to speak to rescuers, police, the French civil aviation authority, the federal prosecutor and EAS, the paper said.
Mr Bussereau confirmed an investigation into the cause of the crash had already begun.
John Key
Prime Minister John Key has expressed sympathy to the families of those killed and phoned Air NZ to offer his support.
A spokesman for Mr Key said he would hold a press conference early this afternoon in Wellington to talk about the crash.
"This is obviously a tragic situation for the families of the people killed and also for the airline. We are in touch with Air New Zealand and the Civil Aviation Authority [CAA]."
Transport Minister Steven Joyce said the New Zealand Government was getting regular updates on the situation.
"Obviously the New Zealand Government has grave concerns and is being updated on developments," he said.
Mr Joyce said it was premature to comment on what shape any investigation might take, although he fully expected New Zealand agencies to play a part.
"But our thoughts right now are with the families, friends, and colleagues of those who were on board."
The Airbus A320
Airbus said the aircraft, delivered in July 2005, had accumulated approximately 7000 flight hours in some 2800 flight cycles. Around 1,960 A320 aircraft are in service with 155 operators around the world.
Air New Zealand owns 10 Airbus A320s and leases two more. They are used on its Tasman and Pacific Island routes and seat around 150 passengers.
The list price of an A320 is around NZ$100 million.
The A320 has had a good safety record since it began flying in 1988. The aircraft is used in more than 70 countries.
One of the worst accidents involving an A320 occurred last year in Sao Paulo, Brazil, when a TAM plane overran the runway on landing, striking an office building. All 181 passengers and six crew on board plus a further 12 people on the ground were killed
- NZHERALD STAFF, AP, NZPA,