The smallest thing that turns a folder of files into a site with a form
The moment a static site needs to receive anything, the usual answer is a serverless function, which means a runtime, a deployment target, a secrets store and something to send the email. That is a lot of apparatus for a form with three fields.
A form endpoint collapses all of it into one URL. Set the form action to that URL, and submissions are captured and forwarded. The site remains a folder of files on a CDN, which is presumably why you chose a static site to begin with.
Spam is the part everyone underestimates
Any form endpoint with a public URL will be found by bots, usually within days of going live. Whatever service you use, the defences that actually work are the cheap ones: a honeypot field a human never sees and never fills, a minimum time between page load and submission, and a server-side check that required fields are present and plausible.
Formspree offers more sophisticated filtering than this does, including captcha integration, and on a high-traffic public form that difference is worth paying for. Be honest with yourself about which kind of form you are building.