<?xml version="1.0"?>
<config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="../../../../../lib/internal/Magento/Framework/ObjectManager/etc/config.xsd">
    <preference for="MagentoContactBlockContactForm" type="[namespace][modulename]BlockContactForm" />
</config>

<?php

namespace [namespace][modulename]Block;

use MagentoFrameworkViewElementTemplate;

class ContactForm extends MagentoContactBlockContactForm
{

    public function __construct(
            TemplateContext $context,
            MagentoDirectoryBlockData $directoryBlock,
            array $data = []
    )
    {
        parent::__construct($context, $data);
        $this->_isScopePrivate = true;
        $this->directoryBlock = $directoryBlock;
    }

    public function getCountries()
    {
        $country = $this->directoryBlock->getCountryHtmlSelect();
        return $country;
    }
    public function getRegion()
    {
        $region = $this->directoryBlock->getRegionHtmlSelect();
        return $region;
    }
}

<?php
$countryList=$block->getCountries();
$regionList=$block->getRegion();
?>
<div class="field country">
    <label class="label" for="country"><span><?php echo __('Country') ?></span></label>
    <div class="control">
        <?php echo $countryList?>
    </div>
</div>
<div class="field country">
    <label class="label" for="region"><span><?php  echo __('Region') ?></span></label>
    <div class="control">
        <?php echo $regionList?>
    </div>
</div>

$(document).on('change','#country',function() {
    var param = 'country='+$('#country').val();
    $.ajax({
        showLoader: true,
        url: YOUR_URL_HERE,
        data: param,
        type: "GET",
        dataType: 'json'
    }).done(function (data) {
        //data.value has the array of regions
    });
});

public function __construct(
        Context       $context,
        MagentoFrameworkControllerResultJsonFactory    $resultJsonFactory,
        MagentoDirectoryModelRegionFactory $regionColFactory,
        PageFactory $resultPageFactory
    ) {
        $this->regionColFactory     = $regionColFactory;
        $this->resultJsonFactory            = $resultJsonFactory;
        parent::__construct($context);
    }

    public function execute()
    {
        $this->_view->loadLayout();
        $this->_view->getLayout()->initMessages();
        $this->_view->renderLayout();

        $result                 = $this->resultJsonFactory->create();
        $regions=$this->regionColFactory->create()->getCollection()->addFieldToFilter('country_id',$this->getRequest()->getParam('country'));
        return $result->setData(['success' => true,'value'=>$regions->getData()]);

    }

In Phtml
    <div class="field company required">
                <label class="label" for="company"><span><?php echo __('Company') ?></span></label>
                <div class="control">
                    <input name="company" id="company" title="<?php echo __('company') ?>" value="" class="input-text letters-only" type="text" data-validate="{required:true,'letters-only':true}" style="width:400px"/>
                </div>
            </div>

            <div class="field country required">
                <label class="label" for="country"><span><?php echo __('Country') ?></span></label>
                <div class="control">
                   <?php echo $countryList?>
                </div>
            </div>


            <div class="field region required">
                <label class="label" for="region"><span><?php /* @escapeNotVerified */ echo __('State/Province') ?></span></label>
                <div class="control">
                    <?php echo $regionList?>
                </div>
            </div>
<script>
    require(["jquery"], function ($) {
$(document).on('change','#country',function() {
            //alert($('#country').val());
            if(document.getElementById('states')){
                document.getElementById('states').value = '';
            }
            if(document.getElementById('state')){
                document.getElementById('state').value = '';
            }
             var param = 'country='+$('#country').val();
             $.ajax({
                     showLoader: true,
                     url: '<?php /* @escapeNotVerified */ echo $block->getCatalogrequest(); ?>',
                     data: param,
                     type: "GET",
                     dataType: 'json'
             }).done(function (data) {

                 if(data.value=='')
                 {
                     $('.field.states.required').show();
                     $('.field.region.required').hide();
                 }
                 else
                 {
                    $('.field.states.required').hide();
                    $('.field.region.required').show();
                    $('#state').empty().append(data.value);
                 }
            });
    });
    });
</script>