The core samples will provide a record of how the composition of the air and ice changed over the past 150 years, revealing levels of sulphur and nitrogen dioxide pollution as well as the effect of specific events such as the Chernobyl nuclear disaster in 1986.
The cores will be airlifted in isothermal containers and stored under 10m of Antarctic snow, at around -54C, to avoid the risk of a freezer breakdown or power cut were they to remain in France.
It is hoped this will preserve them for centuries.
Scientists believe all France's Alpine glaciers up to 3500m will have vanished by the end of this century.
"At the Col du Dome, we measured a temperature increase of 2.7F (1.5C) in the space of 10 years," said glaciologist Jerome Chappellaz.
He said degradation starts when surface water melts, then seeps into lower layers and alters the "chemical memory" of the ice.
