Whenever Firefox is finished downloading something, it automatically opens up the ‘Downloads’ window to let you know. Or, if you had disabled showing the ‘Downloads’ window or had it minimized during the download (s), then Firefox still gives you a notification on your screen.
If you however have disabled showing the ‘Downloads’ window (because sometimes it is kinda distracting) & would also like to replace that notification with the native desktop notification system in Ubuntu’s Unity desktop, then why not try ‘GNotifier’.
Please remember that, unlike the default ‘download completed’ notification which also gives you a clickable link for opening the ‘Downloads’ window, this one only gives you a notification, but it is still kinda pretty though ;-).
Anyhow, Firefox will still open the ‘Downloads’ window and unless you have disabled it, you can open the downloaded files with ease.
It only runs on Firefox 17.0 or newer, the developer says it runs on Gnome (so perhaps it’ll run on Gnome Shell too ?) and once installed, you don’t have to restart the browser as well. If interested, then please download it from this page.