Wordpress: Add custom Class to Contact Form 7 <form> tag

functions.php

<?php

add_filter( 'wpcf7_form_class_attr', 'custom_custom_form_class_attr' );

function custom_custom_form_class_attr( $class ) {
  $class .= ' nice';
  return $class;
}

?>

Please check this link: http://contactform7.com/faq/can-i-add-id-and-class-attributes-to-a-form-element/
This will give you overall information what you want.

Form specific:
[contact-form-7 id="1234" title="Contact form 1" html_id="contact-form-1234" html_class="form contact-form"]
Field specific:
[text* first-name class:full class:field placeholder "FIRST NAME"]

Add class to submit button,
[submit class:btn class:btn-primary "Send"]

Please check this link: http://contactform7.com/faq/can-i-add-id-and-class-attributes-to-a-form-element/
This will give you overall information what you want.

Form specific:
[contact-form-7 id="1234" title="Contact form 1" html_id="contact-form-1234" html_class="form contact-form"]
Field specific:
[text* first-name class:full class:field placeholder "FIRST NAME"]

Ty ! it works for me !