So you got yourself a nice static site, and you want to give your audience a chance to talk to you (directly) with a simple contact form, something you might be used to having used wordpress, php, and a database.
Except there ain't no database here. Even less php back end. Hence you've got to rely on other ways to get personal messages sent to you.
Formspree - Functional HTML forms
When I stumbled upon Formspree, it did look like the perfect match.
Side note: Kudos to the crew that put the site together. Minimalistic, straight to the point and no fuss around the subject.
So, formspree is a tool apparently maintained by a community of developers, clearly stating no contents of the form submissions are stored (emails are sent using Mailgun's API).
You do think about privacy, but not for long. First of all, you ain't giving much away, api or not. Folks are going to initiate discussions in a few words then you take over the talk, privately. No need to be paranoid... especially if (unlike me), you are giving away most of your life to facebook.
Just follow the steps described. Everthing works as expected. Add form elements and don't forget to give them a name, they'll be automatically taken into account during form submission.