It was the Lodge of Perfection in London, associated as The Philadelphic Society, that sponsored the Kelpius journey of Rosicrucian emissaries to America.  By Sasche's translation, it was a "Lodge of Perfecti."  The great lodge in France, too, by translation was a "Lodge of Perfecti". 

This is fairly objective information linking Benjamin Franklin and the Rosicrucian movement—his signature on the ledger of the great French “Lodge of Perfection” or Lodge of Perfecti.  While both Martinists and Rosicrucians were known to meet at the same Lodge in France, it can be understood that various initiatic orders were represented together in a conventical representing one Order.  "Out of one many" is a phrase coined as an American motto, but it is also a fact of Rosicrucianism.  The Order of the Quest, attributed to Franklin by Hall, was an even more initiatic order that was even more exclusive based upon various secret factors about the brethren.

The Rosicrucians centuries ago functioned as a network of initiatic individuals with a mutual spiritual objective of individual freedom in matters of religion.  Those individuals who came into contact at any level with individuals sharing that objective, joined in doing that which each was capable of accomplishing in their respective individual lives. 

In any case, Franklin was clearly in fraternal contact with other Rosicrucians who were members of the Rosicrucian movement, in order to be in attendance at a conventical of the French Lodge of Perfection. 

The Lodges and Chapters of Perfection by various names, were part of a secret network of fraternal individuals of esoteric adepts working privately toward perfecting the process of spiritual enlightenment and understanding of humanity. 

In the 17th Century, one of the vehicles of the Rosicrucian movement was the secret network of Lodges and Chapters of Perfection, were the individuals of  the Johannes Kelpius.  In America these perfecti or adepts were known as "the Woman in the Wilderness," and, also, they were known as "The Order of the Mustard Seed".  Kelpius taught universal doctrines under Rosicrucian Jacob Boehme's writings that explained principles of Christianity.   Another later was the Rosicrucian "Zionitic Brotherhood" functioning separately from the German Baptist teachings of Beissel at the Ephrata Cloister.