JotForm is a free online form builder which helps you create online forms without writing a single line of code. No sign-up required.
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I am not quite sure if I understand your concern correctly. If you would like to have a pop-up form on your website using JotForm, you can embed using the Lightbox embed code, Feedback embed code or the Pop-up embed code. You can find it under the "Publish" wizard:
Copy the embed code you like and paste it in your website page.
Here's a guide on how to create a lightbox embed code: https://www.jotform.com/help/220-How-to-Create-a-Lightbox-Form
Here's a guide on how to embed your form as a feedback button: https://www.jotform.com/help/93-Creating-a-Feedback-Button
Let us know if that works or if I misunderstood your concern.