Finding out whether you’re running 32-bit or 64-bit Firefox is not an easy task, you need to visit about:support page and look for User Agent String field under Application Basics. If UA String shows Win64, then you’re using 64-bit Firefox, if it contains WOW64, then you’re using 32-bit Firefox on a 64-bit Windows.

This digging and understanding no longer required in future with Firefox 51 version, as Mozilla will display the build architecture (32-bit or 64-bit) of Firefox browser in the about Firefox window — to open this, click on menu, click on ? and select About Firefox — along with version number and what’s new link – latter is displayed to beta and release channel users only, check the below screenshot.

Firefox 51 about window showing 64-bit as build architecture.