Static sites are a great option for simple websites nowadays, but the lack of form handling can be an annoying hurdle if the site needs to handle form submissions. Here are a few options for handling forms on a static site:

• Netlify Forms - If using Netlify, Netflify Forms can handle form submissions. Under 100 submissions a month is free currently (but that will probably change or go away in the future).
• Formspree - Looks like they'll only email you the form data.
• FormKeep - Another SAAS option with greater extensibility and integrations for popular services like Salesforce, Trello, etc.
• Kwes - Another SAAS with validation, spam protection, and integrations with popular form data destinations.

There are likely an abundance of similar SAAS products enticing people with free tiers and hoping their usage will bump them into paid tiers. If one needed to service a number of static sites and preferred to keep the form data and submission infrastructure in-house, it would not be out of the question to roll one's own custom solution.