Your code snippet is all okay. I have tested it, forms are getting submitted, and nothing wrong except the way you implement the “_next” feature. As FormSubmit documentation clearly mentioned you have to provide an alternative URL not just a path or file, it should be a URL.
<input type="hidden" name="_next" value="https://yourdomain.co/thanks.html">
Please change the hidden filed in your form to:
<input type="hidden" name="_next" value="https://yourdomain.co/message_sent.html">
and that should probably work fine.
FormSubmit documentation: https://formsubmit.co/documentation
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