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Emily's mother, Nicky, has said that her family are on their way to meet mountain rescue workers in order to "get a better picture of exactly what happened".
Emily Watts, who is also known as Mimi, is an experienced snowboarder and had been working at a ski resort in the Chamonix Valley for a couple of weeks before the accident.
Emily's aunt said she was injured on the first day of the season.
Emily Watts' aunt has said that she believes her niece is not likely to recover after suffering a cardiac arrest in the French Alps.
Shona Pollock said that Emily's brain was starved of oxygen for around 45 minutes before a rescue team reached her. "She's on a life support machine but it won't be for long," she said.
Ms Pollock described Emily as "outgoing" and "plucky" and said that she loves the mountains.
Emily Watts' parents, Nicky and Dominic, along with her 27-year-old brother Rory, have all travelled to the hospital in Annecy where she is being treated.
It took several days for French authorities to notify her parents because she was not wearing any form of identification.
A British student who was left critically ill after a snowboarding accident in the French Alps is still fighting for her life, her family said today.
Emily Watts, known as Mimi, fell headfirst into a snowdrift and was stuck for about 45 minutes following the fall in Chamonix on Saturday.
By the time emergency crews arrived, the 26-year-old, from Lavenham, in Suffolk, had suffered a cardiac arrest, prompting fears of brain damage.