Fran. 'Tis a ridiculous thing for a man to be his own chronicle: I did never wash my mouth with mine own praise, for fear of getting a stinking breath.
Marc. You 're too stoical. The duke will expect other discourse from you.
Fran. I shall never flatter him: I have studied man too much to do that. What difference is between the duke and I? no more than between two bricks, all made of one clay: only 't may be one is placed in top of a turret, the other in the bottom of a well, by mere chance. If I were placed as high as the duke, I should stick as fast, make as fair a show, and bear out weather equally. (5.1)
Francisco is impersonating a Moor (North African) named "Mulinassar" when he says these lines, but they seem to match his real philosophy well enough. He's a complicated figure: Francisco is seeking revenge against the people who murdered his sister—an understandable if not extremely enlightened form of human activity—and he plots and schemes with the Cardinal Monticelso, who doesn't tend to behave in a way that's particularly appropriate for a Man of God.
But Francisco seems a bit less corrupt than most of the other characters in this play. As demonstrated by the quote, he lives by a code, and he's skeptical of people who pursue power or view themselves as inherently superior. Also, he's resourceful (as evidenced by the fact that he's pulled off a pretty good disguise) and very devoted to his family members.
Francisco—along with the Cardinal—doesn't get any kind of comeuppance in the end. He's already suffered enough, given the fact that Brachiano murdered his sister, and his act of revenge seems to be justified. Lodovico is Francisco's "fall guy"—he takes the punishment for going outside the law.
Francisco is also skeptical of figures like Monticelso. When the Cardinal gives him a book listing all the known-criminals who might help them in pursuing revenge, Francisco comments (privately and to himself):
See the corrupted use some make of books: / Divinity, wrested by some factious blood, / Draws swords, swells battles, and o'erthrows all good. (4.1).
His sibling bond with Isabella is close, and is major factor in leading him to pursue revenge for her murder. At one point, Francisco has a vision of Isabella's ghost (though he blames it on his own melancholy frame of mind), which provokes him to sadness. But he picks himself up, reminding himself that there are bigger fish to fry:
Out of my brain with 't: what have I to do / With tombs, or death-beds, funerals, or tears, / That have to meditate upon revenge? (4.2)
That's right Francisco, carry on; ghosts or not, there's nothing to linger on here.