The barrage came down abutting to Valfrejus, not far from the Italian border, breadth some 50 soldiers were training off-piste.
Search dogs and helicopters anon began searching for the soldiers.
Last week, two academy pupils and a Ukrainian day-tripper were dead by an barrage nearby.
A abecedary is beneath analysis for assassination afterwards he allegedly led his pupils on to a bankrupt ski run anon afore the barrage in Les Deux Alpes, 124km (80 miles) abroad from Valfrejus.
Heavy snow has collapsed in the Savoie arena recently.
About 10 of the aggressive aggregation were anon begin by rescuers - but 5 had gone into cardiac arrest, and died.
The soldiers were skiing in the Petit Argentier breadth at a acme of 2,200m (7,200ft) if they were bent up in the barrage anon afore 14:00 (13:00GMT), bounded letters said.
The soldiers were associates of the 2nd Adopted Engineer Regiment based at Saint-Christol in southern France. They had been training at France's civic centre for abundance warfare at Modane.
The accumulation was a admixture of veterans and new recruits, administrator Julien Aubert told France's BFM television.
The French Adopted Legion was set up in the 19th Century for adopted nationals to serve in the French armed forces, although it is accessible to French citizens.
The nationalities of the victims were not anon known.All the soldiers demography allotment in the contest had barrage apprehension kits, and rescuers were on the arena aural minutes, letters said.
Two of those begin by rescuers were taken to hospital adversity from hypothermia.
"For now the affairs aren't actual clear," Major Herve Pujol from the CRS accomplishment aggregation told BFM-TV.
"We're still aggravating to backpack out the accomplishment and aggravating to calculation anybody in the area, to apperceive if we still accept humans there who've been buried."
Police in Lyon are accepted to handle the analysis into the blow and Defence Minister Jean-Yves Le Drian will appointment the arena on Tuesday.
Prime Minister Manuel Valls said his thoughts were with "the injured, families, brothers in arms".
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