Add the following script using the wp_footer hook or into an existing javascript .js file to advance the cursor when the enter key is pressed.
jQuery(document).on('keypress','.gform_wrapper',function(e){ var code = e.keyCode || e.which; if (code==13 && !(jQuery(e.target).is("textarea,input[type='button'],input[type='submit']"))){ e.preventDefault(); var li = jQuery(e.target).closest('.gfield_visibility_visible'); var nxtli = li.next('.gfield_visibility_visible'); var nxt = nxtli.find('.ginput_container'); var f = nxt.find('input[type=text],input[type=password],input[type=radio],input[type=checkbox],textarea,select').filter(':visible:first'); if (f) f.focus(); return false; } });;