When you are filling in the form, before you submit, do you see a CAPTCHA test (whether the Google ones or some other service)? If not, something might be blocking it. Firefox's Tracking Protection feature, and extensions that counter ads and tracking, may break websites that embed third party content (meaning, from a secondary server). (A) The shield icon toward the left end of the address bar usually turns a bit purplish when content is blocked. Click the icon to learn more or make an exception. See: [[Enhanced Tracking Protection in Firefox for desktop]]. (B) Extensions such as Adblock Plus, Blur, Disconnect, DuckDuckGo Privacy Essentials, Ghostery, NoScript, Privacy Badger, uBlock Origin or uMatrix may block required elements on a site. Usually you can find a toolbar button for each add-on to manage blocked content in a page. There may or may not be a number on the icon indicating the number of blocked items; you sometimes need to click the button to see what's going on and test whether you need to make an exception for this site. Any improvement?