The man posted a message on social media on Wednesday saying he was coming down from the 4,810-metre (15,780-feet) summit of western Europe's highest peak but needed help.
Thursday was his fourth night on Mont Blanc alone, Le Parisien reported.
Rescue helicopters are unable to fly because of poor visibility and rain with conditions only expected to improve on Saturday.
Patrice Ribes, head of the local police rescue service, said the climber "could survive several days" providing he had found shelter and had enough water.
"As soon as we can, we'll go looking for him," he added.
Police have posted a Facebook appeal to help them in their search (see below).
- Rescuers find missing South Korean climber dead on Mont Blanc
- Human remains found on Mont Blanc may belong to Air India victims
This isn't the first time Mont Blanc has made the headlines this summer, with two Germans found dead on Wednesday after dying of hypothermia.
Earlier in August, The Local reported on the death of a South Korean mountain climber on the peak.
And in late July, The Local reported on human remains thought to belong to passengers killed in one or other of two Air India plane crashes more than 50 years ago discovered on Mont Blanc.