Can I add id and class attributes to a form element?

Yes. You can add any id and class to a form by adding the html_id and html_class attributes into a [contact-form-7] shortcode.

Example:

[contact-form-7 id="1234" title="Contact form 1" html_id="contact-form-1234" html_class="form contact-form"]

Just another contact form plugin for WordPress. Simple but flexible.