You should put it inside ‘the_content’ hook.
1)Create first plugin which has the form that proccess simple form submission.
2)And then call that page in iframe window.Like this:
<---YOU DIV STARTS HERE FOR POPUP WINDOW-->
<div id="iframeclasses">
<?php add_thickbox(); ?>
//Your form link
<a href="https://wordpress.stackexchange.com/questions/248296/YOUR_LINK_GOES_HERE&KeepThis=true&TB_iframe=true" class="thickbox">
</div>
3)iframe window open by following code.
<input type="submit" name="submit" class="button button-primary emailbtn" value="<?php _e('YOUR_BUTON_TEXT', 'TEXTDOMAIN')?>" >
</div>
//your div close here