In order to continue playing FarmVille 2 on FireFox Browser, you need to enable Adobe Flash on the browser.
Here are the steps to enable Adobe Flash on Firefox:
Load FarmVille 2 https://apps.facebook.com/farmville-two/ on your Firefox Browser, and open the 'menu' found on the extreme right side of the address bar. Click to open menu as illustrated below.
Locate and Click “Add-ons” from the menu options:
Here on the Add-ons Manager, Click on “Plugins” found on the left side pane.
Select the “Shockwave Flash” plugin and Click “Always Activate” from the list of options in the drop-down.
Reload the page and continue playing FarmVille 2!