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SurveyJS
Open-Source JSON Form Builder to Create Dynamic Forms Right in Your App. With SurveyJS form UI libraries, you can build and style forms in a fully-integrated drag & drop form builder, render them in your JS app, and store form submission data in any backend, inc. PHP, ASP.NET Core, and Node.js.
Mailjet provides a JavaScript SDK that actually makes integrating with its API pretty easy. You'll need your Mailjet API key and secret key, which you can find in Mailjet under Account Settings and then choose "API Key Management (Primary and Sub-account)" under REST API. Place those in an environment variable.
Every Netlify function has a URL that you can post to, so it's just a matter of making the HTTP request. The script is pretty simple, it adds a submit event listener to the form, gathers the data and then uses Axios to make the request to the function. Do I need Axios? No, but it works.