The name "Bretagne" is used to qualify the Isle now called "Great Britain"
in history courses in France, during the period 55BC-5th Century AD.
During the same period, the dwellers of the south part of the Island
are referred to as "Bretons" (Brittons in English), see for instance
the (maybe) famous French Comics "Asterix etLes Bretons" the action
of which takes place in England.
After the Britton emigration to Armorica, the terms "Bretagne" and "Bretons"
corresponded to this part of France. In French, it's rather confusing,
but not in English because you have different names for the two periods :
Before 500 AD After 500 AD French equivalent
(in England) (in France)
Britain, Britannia Brittany Bretagne
Britons Bretons Bretons
When Armorica became "Bretagne", Britain got called "Grande-Bretagne".
but, the inhabitants of the latter were not named "Grands Bretons" (except
as a joke) but "Britanniques".
I hope this disgression in french vocabulary will have interested you.