No I don't know the specific inclinations of Franklin. However, the idea of Deism in which a god creates the universe and then abandons it from any further meddling was in favor with Deists. The notion of religion or churches are not abhorrent to Deists. They just didn't subscribe to a personal God who watched over your every move or directed your actions. I think the Deists saw value in the God of Abraham who was the final arbiter in good and evil rather than an absolute monarch.
Remember, the Book of Moses sets down for the first time a history, the God of the Jews, and a set of laws. It gave the Jews self determination without the need of a human authority assuming godlike qualities like the Pharaoh. The Jews placed certain rights of authority beyond any human, and followed God's law.
The founding fathers took this one step further and defined those inalienable rights and created a living document and framework for it to evolve. Their intent is not to live under the rule of an absolute monarch or a ruler falsely claiming godlike qualities.
The two Adams presidents belonged to a Unitarian Church. They are now buried within it in Quincy, Massachusetts. In their time Unitarians still identified as Christians. Less than 100 years later the Unitarians no longer considered themselves as Christians. They identify more with humanism than religion. They claim to accept all religions but really abhor the idea of a personal god. I would say they identify with Deism but not with the inalienable rights of man. They are now full blooded socialists.
You would probably be interested in his autobiograpy. I read it last year; don't have it any more. I would say from my memory that he wouldn't be the kind of Deist who thinks God has no hand in the affairs of men.
***When an impasse had been reached at the Continental Congress, Benjamin Franklin called for prayer with these words:
"I have lived, Sir, a long time, and the longer I live, the more convincing proofs I see of this truth, that God governs in the affairs of men. And if a sparrow cannot fall to the ground without His notice, is it probable that an empire can rise without His aid? I therefore beg leave to move--that henceforth prayers imploring the assistance of Heaven, and its blessings on our deliberations, be held in this Assembly every morning before we proceed to business"