AElflaed note: This was lifted from Cathyn's website so I could edit and preserve it. It might still be out there elsewhere as well.
In modern terms, Franchise is the polar opposite of "what's in it for me?" This is not to say that when practicing the virtues one is wrong to consider personal or spiritual growth, which are the real essence of practicing the virtues. Becoming virtuous for virtue's sake alone is the goal. To be virtuous for the sake of having others notice you being virtuous, or to win acclaim and renown lacks Franchise.
To cite a real world example of this, let's briefly examine the Knightly Virtue of Largesse. Largesse is sharing with others within the prudent bounds of one's resources. Making a charitible donation to the United Way is one form of Largesse, which in some lists of virtues is actually called Charity. If you made that charitible donation out of a genuine concern for your fellow man, you are also practicing Franchise. If, however, you made that donation for the tax break, that is the "what's in it for me?" part of your generosity, and singularly does not display Franchise.
As you think on this virtue, it is clear to see that this is the most important of the virtues, as one's motivation for being virtuous is as important as being virtuous itself is.