They were aged between 58 and 73.
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President of the French Federation of Alpine and Mountain Clubs, Georges Elziere, confirmed at the association's 15th National Congress in Nantes on Sunday local time that the skiers were members of the organisation.
"Six skiers - members of Alpine Clubs Guillestrois, Argentiere-la-Bessee and Briancon - died Saturday January 24th in an accident over Ceillac [Hautes-Alpes], in the valley Bachas," the club said.
Mr Elziere expressed his condolences and support for the families, assuring them of the club's sympathy and solidarity.
Ms Nash, who lived in L'Argentiere-la-Bessee, ran a physiotherapy and osteopathy clinic. She had one child.
She moved to France in the early 1990s.
A Ministry of Foreign Affairs and Trade spokesman said it was aware of her death.
"The New Zealand Embassy in Paris has followed up with the local French authorities who have confirmed the death of Carol Nash," he said.
The ministry was in contact with Ms Nash's family, who had requested privacy, he said.
The deadly avalanche was 300m wide and 900m long, French media reported.
Pierre Besnard, the Haute-Alpes prefect, said the avalanche was caused by a hard slab of snow cracking and falling.
Mountain rescuers - including 18 searchers and two dog handlers - began searching for the skiers on Saturday afternoon local time, after other members of the club reported them missing when they failed to return from the trek, which started at the Ceillac ski station.
They worked in treacherous conditions overnight to find the skiers, with three bodies located shortly after midnight on Sunday local time, with the remaining three discovered nearby later that morning.
An investigation into the incident was under way, the Guardian reported.
Michel Vauzelle, president of the Provence-Alpes-Cote d'Azur region where the avalanche occurred, expressed his "sincere condolences" to the families of the victims.
It was a "terrible tragedy".