Title is pretty self explenatory. I use wordpress v4.9.8 with Rocked free theme. I installed contact form 7, no other plugins, and put the shortcode of the base form in a new custom_html widget in the footer-1 area.
Instead of the form, it just shows the raw shortcode. Also tested with twenty-seventeen so I dont believe its the themes fault.
shortcode: [contact-form-7 id="5" title="contact form 1"]
For anyone stumbling upon this from Google, it seems to be a bug in the latest contact form 7 update. The solution is to use the Text widget instead of custom html.
source: https://wordpress.org/support/topic/contact-form-7-not-working-in-footer-after-update/