If you have previously disallowed Discord access to your mic in Firefox, you will need to enable it in the Firefox Permission Settings before being able to use it.
To enable your mic in Firefox follow the following steps:
1. Open the Firefox Permissions Manager. To do so, type the words about:permissions into the location bar as if it were a website and hit Enter. The current tab will be replaced by the Permissions Manager.
On the left hand side you'll see a search bar with a list of all the websites you've been to below it. The right hand side lists the various website permissions that Firefox stores.
2. Find or Search for Discordapp.com among the list of sites.
3. In the 'Use the Microphone' section, select 'Allow' from the drop down menu.
4. Return to the Discord app and unmute your mic.
Your mic should now be working correctly in the Firefox browser.