The first problem is the path, you need override the component from: your_site/components/com_contact not your_site/administrator/components/com_contact
Also the code for the template must be in: your_site/templates/your_template
Here you have an example:
https://stackoverflow.com/questions/20586581/adding-fields-to-joomla-3-x-contact-component
Other possible solution is via plugin, find more info here: https://docs.joomla.org/Adding_custom_fields_to_core_components_using_a_plugin
