The five climbers and their guide, all aged between 27 and 45, went missing due to bad weather late on Tuesday, BBC reported.
The bodies were reportedly found on Wednesday after a rescue team was sent to Aiguille d'Argentiere, a 3,900m (12,800ft) peak in the Mont Blanc range.
According to French mountain rescuers, the group died after falling 250 metres.
The climbers' identities have not yet been confirmed.
An investigation is underway into the possible cause of the deaths.