Also, why doesn't the Champagne Bureau complain about an infringement on their turf?
Here's the basic answer. There are six grape-growing regions in Cognac, and the two considered the best are called Grande Champagne and Petit Champagne. A Cognac called "Fine Champagne" is made from grapes from both regions, at least 50% from Grande Champagne.
Now, how did these regions come to be named that? Well, the answer people in Cognac give you is that "Champagne" comes from a French word for chalky soil, which makes sense.
However, there's a link missing in this history of the word. The Champagne region where the bubbly comes from was named by the Romans after Campania, south of Rome, because they thought the rolling hills looked similar. How the word got south to the Cognac region, I don't know.
It's worth noting that for most of their history, the Charente region that includes Cognac has been wealthier and better known worldwide than the original Champagne.
The latter had poor agriculture due to chilly weather and those chalky soils. Wineries there didn't really figure out that terroir could be an advantage until the early 1800s, when the invention of strong glass bottles made it possible to market wine with bubbles -- which was originally considered an unfortunate accident.
Hennessy invented a style called Imperiale for the Russian empress Alexandra Feodorovna, to celebrate the birth of her son, the future Tsar Alexander II. The empress wanted light and clear Cognac, but very old. And this was in 1818, showing that decades-old Cognac was already sought after.
About that time, Veuve Clicquot Ponsardin was inventing the riddling table that made production of Champagne more consistent. My point is that Grande Champagne and Petit Champagne in Cognac could have been named after the larger wine region to the north, but why would the locals want to? The folks in Cognac were the big dogs commercially at the time, the "spirit valley," which still is true today (Grey Goose vodka, Hypnotiq, and a host of other spirits are made there).
"Champagne" on a bottle today gives it international prestige. The Champagne bureau is always fighting companies that try to call their product the "Champagne of beers" or the "Champagne of shampoos."
But about Fine Champagne Cognac, the Champagne Bureau can't complain. Cognac people have been using it since before sparkling Champagne was considered fine.