Few Problems:
1) In the delete form, you have the button and the hidden element both using the same name, files_c:
<form method="post" enctype="multipart/form-data" name="delete-file" class="form-horizontal delete-file" id="delete-file">
<button class="btn btn-danger" name="files_c" id="files_c">Delete File / <?php echo $row_rsEnqDetails['files_c']; ?></button>
<input type="hidden" id="files_c" name="files_c" value="none">
</form>
2) button element types don't actually do any thing. change the button to a submit button, heres an example where i changed the name of the button so the hidden element can remain as is:
<input type="submit" class="btn btn-danger" name="submit_files_c" id="submit_files_c">
3) the hidden element should pass the file name as the value:
<input type="hidden" id="files_c" name="files_c" value="<?php echo $row_rsEnqDetails['files_c']; ?>">