The reason why I ask is because it seems that your theme or some part of your site is wrapping all the text in the Content Fire newsletter form with <code/> tags. This is why the submit button is not working.
Is there any setting on your site that has text auto-wrapped with <code> tags?
There was a little bug on our side that made Content Fire not compatible with Visual Composer but we were able to fix it :) So please update the plugin to version 1.1.4 through the WordPress plugins page in your admin panel.
If you have any other questions please let us know, and if you are enjoying the plugin please be sure to give us a review :)