With App-V prior to version 5 it was not possible to set a virtualized Firefox as the default browser. This is by design. With App-V 5.0 this is not restricted anymore.

This article applies to any Firefox version, but has been written with Firefox 17. 

• Install the AppV 5.0 Sequencer on a workstation with Windows 7 with SP1.
  
  
• Sequence Firefox 17.0.1 with the default settings. Only the update service should be disabled.
  
  
• Install the AppV 5.0 Client on a second workstation with Windows 7 with SP1.
  
  
• Install the virtualized Firefox 17.0.1. with PowerShell:
  

  Set-ExecutionPolicy -ExecutionPolicy Unrestricted
  Import-Module AppVClient
  Add-AppvClientPackage –Path D:\Mozilla_Firefox_17.0.1-AppV5.0_ENG\Mozilla_Firefox_17.0.1-AppV5.0_ENG.appv -DynamicDeploymentConfiguration D:\Mozilla_Firefox_17.0.1-AppV5.0_ENG\Mozilla_Firefox_17.0.1-AppV5.0_ENG_DeploymentConfig.xml | Publish-AppvClientPackage -Global
  ​

• Start Firefox 17.0.1 and made it the default browser.
  
  
• Go to ‘Default Programs’ in the Control Panel
  
  
• Set Firefox as the default program:
  
  
  
• In the Search box enter the webpage to open: www.google.com.
  
  
• The icon is a ‘firefox’ one.
  
  
• And Google is opened with Firefox.

You can only set a virtualized Firefox as the default browser if it has been published globally.