Champagne is related to Cognac in more ways than you might think!
The original meaning of the word
The original meaning of the word Champagne in French is "open country". It's used in many place names in France, which has confused many a tourist. Often deployed in place names that are vast exanses of fields, it pops up all over the country.
In Cognac, with plenty of open country, Champagne is used to name two of the best crus within the Cognac appellation. You can see on the map that the regions appear in concentric circles with the village of Cognac at the centre.
The soils of both Champagne and Cognac are prized for their chalk content
The most prized vineyards in the Cognac region are in Grande Champagne where the soils are predominantly a chalky limestone - another thing in common with the bubbly version of Champagne!
Petite Champagne is next in prestige, sharing similar chalk content with the Grande Champagne region, but with a little more maritime influence. The 3-year, 5-year, and 10-year Cognacs from Conte et Filles are all Petite Champagne.
It is common for Cognac producers to blend juice from grapes in both Grande and Petite Champagne to make what is called Fine Champagne, incorporating the desirable characteristics of the brandies of each region. These blends must be at least 50% Grande Champagne eau-de-vie (the initial spirit distilled from the Ugni Blanc wine). The Heritage Cognac from Conte et Filles is an example of Fine Champagne.
The remaining regions of Cognac: Borderies, Fins Bois, Bons Bois and Bois Ordinaires see reductions in the chalk content of their soil, the further out they extend from Grand and Petite Champagne. Cognac from these regions is less sought after, though usually less expensive.
The official Cognac website has more great information here, though you might want to turn on your browser's translation function.
They also have a high quality pdf of the region map here.