Is the preference for handling certain file types, in this case mp3 (when available), still as it should? See Preferences > General panel > Applications section, as well as the Manage file types and download actions in Firefox support article for more info.

If that doesn’t help, remove the file called handlers.json in your Profiles folder as explained at the bottom of that article.

You can set this pref to false on the about:config page to prevent Firefox from playing media files via the HTML5 media player.

• media.play-stand-alone = false

You can open the about:config page via the location/address bar. You can accept the warning and click "I accept the risk!" to continue.

• http://kb.mozillazine.org/about:config