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This will display on the contact us page, not the CMS page. 

You add the same on the CMS, you need to do either from the module OR changes in the themes\classic\templates\cms/page.tpl

Change

{block name='cms_content'}
      {$cms.content nofilter}
    {/block}

to

{block name='cms_content'}
      {if $cms.id == "1"}
        //Your Form Content
      {else}
        {$cms.content nofilter}
      {/if}
      
    {/block}

Update $cms.id == "1" to your CMS page ID.