ZenCart has a built-in contact form available at ...
http://www.example.com/index.php?main_page=contact_us
which looks like ...

If you don't like the use of contact forms for security reasons or because the sender of the form can easily poses as another person by inputing another email address, etc, then it is possible to disable the contact form by commenting out the code in the file
/includes/templates/template_default/templates/tpl_contact_us_default.php
as shown...

Of course, if you disable this built-in contact form, you would have to add a contact form of your own (perhaps with an EZ-Page) so that customers have a way to contact the store owner.