JotForm is a free online form builder which helps you create online forms without writing a single line of code. No sign-up required.
We believe that if one user has a question, there could be more users who may have the same question. This is why many of our support forum threads are public and available to be searched and viewed. If you’d like help immediately, feel free to search for a similar question, or submit your question or concern.
You can do that by using script embed or iframe method. However, we don't recommend putting your form to an email message because not all email providers allow these kind of emails that has script code or iframe code for security purposes. It will be detected as malicious or suspicious email.
I suggest to share the direct link of the form instead. Here's a guide to get the direct link:
You can also check this guide: How-to-send-a-form-via-email
Hope that helps. Thank you.