This secret society of Sarans and Pan Sarans was formed by war weary members of both civilizations during the in the 7th and last millennium of the Pan Saran/Saran Civil War.
The Sarans believed Earth to be a forgotten Saran colony and secretly visited Earth throughout history. After the revolt of the outer Colonies of the Saran Kingdom led to the formation of the Pan Saran Empire, they too visited Earth (around 50 BC) and observed the Roman Empire dominating ancient Egypt. (Since Saran and Ancient Egypt shared many cultural similarities, the Pan Sarans saw this as an Omen). The Pan Saran Empire in search for an expression of their own identity that set them apart from the Sarans adopted almost everything of the Roman Culture.
They too held Earth in special regard.
This fact led to the formation of a Secret Society with members of both sides seeking a way to end the war by promoting Earth as a common ground.
The BFE, despite its secret status grew in popularity and gained many influential and powerful members of each society.
When it became clear that Earth would be the next target of the Xunx, the BFE managed to convince the Queen of Saran to intervene and send a fleet to Earth with plans to evacuate Earth.
After the Freon Crisis in 2200, the BFE convinced leaders of both civilizations to finally end all hostilities and form a new Union between Earth, Saran and Pan Saran.
(Note: Ugla Mohn, a non humanoid Ult had been observing the BFE and its activities for some time and when the plans of forming the United Stars of the Galaxy became known to him he actively campaigned for the Ult to join as well.)
After the formation of the Union, the BFE changed its status from a secret society to a public one. It exists to this day but is mostly a historical society now.
The BFE still has a small secret arm, that believes the Union should change into an Empire with a Terran Emperor at its top. (See Imperialist Movement)