You see Franklin didn't think that HIS good works merited Heaven, but he thought God would let him in anyway. What that means is that Franklin, like orthodox Catholics and Protestants (and others) thought ultimately God's unmerited grace would get him in. But Franklin also intimated that there were some better than him who perhaps could work their way into Heaven? That's part of what I get out of the quotation featured below.
How does Jesus and "faith" figure in? To Franklin faith was a means to the end of virtue. Good works were an essential component of Franklin's belief in "justification" (if you want to call it that). I don't think Franklin thought Jesus to be an Incarnate God, 2nd Person in the Trinity; in fact he admitted that he "doubted" such a thing. But he did think Jesus the greatest moral teacher of all time. So it stands to reason that if the purpose of faith is morality and Jesus is the greatest moral teacher, various forms Christianity would be valued for that reason.
I don't believe Franklin thought God's "grace" needed to be "channeled" through Christ's atonement. Rather the unmerited grace that got Franklin into Heaven was some kind of mysterious gift of God. Franklin differed with the "orthodox" there.
In a letter he wrote in 1753 (and later sent a copy to Ezra Stiles in 1790) where Franklin conceded that he didn't think his good works merited him Heaven, he also described what he saw as Jesus' role, quoting Jesus Himself.
He profess’d that he came not to call the Righteous but Sinners to Repentance; which imply’d his modest Opinion that there were some in his Time so good that they need not hear even him for Improvement;...This sentiment comports 100% with Jesus as greatest moral teacher, and 0% with orthodox theology. He blatantly said there were some in Jesus' time, so righteous that they didn't need Him.
Think of Ben Hur, who in the story met Jesus at the end and converted. Franklin probably wouldn't have had a problem with this righteous man meeting and following the greatest moral teacher. He probably thought they had a lot in common. However, Franklin would not have thought Ben Hur necessarily needed Jesus.