The agency described the danger as of “exceptional intensity” and said numerous avalanches were expected on Monday evening.
More than 1,800 of these avalanches could take unusual trajectories and may hit roads and villages, the agency said.
Meanwhile the Hautes-Alpes department is on orange alert (one level below red) for avalanches and the Alpes-Maritimes is on orange alert for avalanches and storms.
The public are advised to avoid high roads in the area and to heed the safety advice in ski resorts.
On Monday The Local reported the death of a young British man Owen Lewis, 22, who froze to death after getting lost on his way home from a bar in the ski resort of Risoul.