Hi @Grant, the server side integration for that is not available yet on Webflow side. It sounds like you are going to need a custom mail script to process the post messages for google recaptcha and that part we just do not have made yet.
We are working on our own captcha integration with forms, but we have not server side integration with forms currently :-/
I wish I could give you better news on this. As soon as we have an update to captcha, we will announce it in updates 
Design Responsive Websites - Webflow