At ski resort La Plagne, a British man aged about 50 was buried under snow on Sunday local time, according to a statement from the resort.
French media reported that 52 rescue workers, sniffer dogs and a helicopter were deployed, but it took 50 minutes to find the man trapped under 2.5 metres of snow, and he could not be revived.
In nearby Courchevel, also in Savoie, another person was buried by an avalanche and found dead in the late morning, reports said.
The regional daily Le Dauphiné libéré also reported several injured skiers and snowboarders in resorts at Tignes and Orelle.
A 32-year-old man also died in an avalanche in Vallorcine near the Swiss border, according to media reports citing mountain police.
He had been skiing off piste when the avalanche threw him against a tree. He later succumbed to his injuries, local media reported.
The day before, three people had already died in avalanches in the region.
More avalanches were reported across Savoie on Sunday, prompting the local officials to call on locals and tourists to "be extremely careful".
"By 12.30pm, rescue services had already been deployed to six avalanches on different mountain massifs," the prefect of Savoie posted on Facebook.
Avalanche danger is set to remain high across all mountain groups in the coming days and local officials are strongly advising against venturing off piste.
In the Austrian state of Tyrol, three people were injured in three avalanches on Sunday, the Tyrol operations centre said. A woman was in critical condition, it added.
The avalanche risk in western Tyrol and in the state of Vorarlberg is expected to remain high at the start of the week, according to the latest assessments.
In the Allgäu Alps in Bavaria and in Switzerland the risk was downgraded from high to considerable.
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