Thunderbird needs to be told about the browser to use.
Open Thunderbird, got to Edit -> Settings. The icon on the right in the dialog popping up leads to extended settings (I'm using a German Thunderbird and don't exactly know what yours might say).
In the general tab there's a button which loads about
:config; click this, it opens a list of settings with key - value pairs. There's a line saying 'filter', type 'protocol' in there. There should be the following entries (among others):
network.protocol-handler.app.http xxx string firefox
network.protocol-handler.app.https xxx string firefox
The xxx is for 'Standard' or 'User'. It is possible that neither entry exists, in which case you have to create them by right-clicking the white space in the list, then choosing new -> string. In the first window, enter the name exactly as above (network...http), then click ok; next, enter the value (firefox). Then do the same for the https entry. You don't set the Standard / User part.
If there are no typos you should then be able to use links in e-mails after a restart of Thunderbird.
Note that your executable for firefox might well have a different name, for instance firefox-bin. You can find out by looking at the setting for the executable in a working Firefox icon (right-click, properties). Of course you can use the executable of any other browser just as well.