You need to override controller which sends email for contact us form.
Magento\Contact\Controller\Index\Post.php
In this file line number around 57 you will get a code which sets template id.
$transport = $this->_transportBuilder
->setTemplateIdentifier(<YOUR_EMAIL_TEMPLATE_ID > )
->setTemplateOptions(
[
'area' => \Magento\Backend\App\Area\FrontNameResolver::AREA_CODE,
'store' => \Magento\Store\Model\Store::DEFAULT_STORE_ID,
]
)
->setTemplateVars(['data' => $postObject])
->setFrom($this->scopeConfig->getValue(self::XML_PATH_EMAIL_SENDER, $storeScope))
->addTo($this->scopeConfig->getValue(self::XML_PATH_EMAIL_RECIPIENT, $storeScope))
->setReplyTo($post['email'])
->getTransport();
In this code replace it with your email template id. so your email template will be used to send emails.