The contact shortcode should work.
Can you pls try the invent theme contact form in the “Contact Forms” ?
Or Pls try to create a new contact form 7 and pls paste the below code in the form field and see if that makes any change or not ?
[text* contact_name placeholder "Name:"]
[email* contact_email placeholder "Email:"]
[tel* contact_phone placeholder "Phone:"]
[url contact_url placeholder "URL:"]
<p class="full-width text-area">[textarea contact_message 40x6 placeholder "Message:"]</p>
<p class="full-width">[submit class:button class:large class:default "Send the message"]</p>
<div class="clear"></div>