The view you want to change is the standard Partner form view:

base.view_partner_form

Look for the section:

<notebook colspan="4">                        
    <page string="Contacts &amp; Addresses" autofocus="autofocus">
        <field name="child_ids" mode="kanban" 
               context="{'default_parent_id': active_id, 'default_street': street, 
               'default_street2': street2, 'default_city': city, 'default_state_id': state_id, 
               'default_zip': zip, 'default_country_id': country_id, 
               'default_supplier': supplier, 'default_customer': customer, 
               'default_lang': lang,}">
            ...
            <form string="Contact / Address">
            
            <!-- this is where the form view that pops up is defined -->

You can define a Form view for a child record inside the Form view for the parent record.