I had this problem on my Gentoo boxes where you click on a link sent in an email and it opens nothing. This is similar to a reverse problem of opening mailto links in Thunderbird found here. Just follow these directions and soon you will have your links opening in Firefox (or a different browser with a slight modification).

You will need to go into your Thunderbird profile to do this. In your home directory, you should have a hidden directory named .thunderbird. If you don't have that, you may have something similar like .mozilla-thunderbird. Open the .thunderbird directory.

In the .thunderbird directory, you should have something similar to this:

-l ~/.thunderbird

$ ls -l
total 9
-rw-r--r-- 1 jdeiman jdeiman 335 Feb 27 12:06 appreg
drwx------ 3 jdeiman jdeiman 160 Feb 27 15:00 eclipse
drwx------ 6 jdeiman jdeiman 960 May 10 15:02 nnx9f70w.default
-rw-r--r-- 1 jdeiman jdeiman  94 Feb 27 12:06 profiles.ini

Your default profile directory is the one entitled <some characters>.default. Open that directory.

Now, all that's left is to create a file called user.js and put the following lines in it (modify appropriately to reflect your path to the firefox binary):

user_pref("network.protocol-handler.app.http", "/usr/bin/firefox");
user_pref("network.protocol-handler.app.https", "/usr/bin/firefox");

Now, just restart Thunderbird and your links should open up in Firefox.