Because it’s not possible to process the data in a web form on a static website you have to rely on a third party service. In the attachment above you can find the comparison of five of such services. The services that I compared are: Formspree, Kwes Forms, Getform, 99Inbound and Jotform.
I hope this comparison can help you choose the right service.
Above I suggest that’s only possible to process the data in a form by using a third party service. Of course this isn’t completely true because it’s still possible to add a PHP script to your website (for example in a subdomain of your website). If this is what you want to do then PHPMailer is probably your best option.
You can find more information about PHPMailer here: