Without knowing which bits from which Application.cfc you need to re-use, it's difficult to answer this.
However you cannot have multiple inheritance in CF. I guess you know this.
You could conceivably create a new CFC in your sub app which extends the one in the main app, and then create an instance of that wihthn your sup-app's Application.cfc. You can then call its public methods and access its THIS scope as needs must.
And your sub-app can then extend the Fusebox one as per normal.
Or, possibly, do it the other way around, depending on which makes more sense.
Other than that, you could refactor the bits you need from the main app into some other construct (and include file, a different CFC or something), and then call that code from each of the main-app and sub-app, and again extend Fusebox from the sub-app. Obviously this means monkeying with the main app, and regression testing again, etc.