I had a similar problem. This can be fixed by updating the ID field in your short-code. Many older contact forms will either be missing the ID field, or the ID field will be a shorter number because it seems that CF7 at some point reindexed all contact forms to use a 4 digit ID.
Old Tags may look like:
[contact-form-7 id=”1″ title=”Contact Us”] or [contact-form-7 title=”Contact Us”]
But if your go to Contact > Contact Forms, you will see the proper short-code to use and it will look more like this:
[contact-form-7 id=”1401″ title=”Contact Us”]
Just copy the new short code over your old one and the error should go away without having to downgrade to an older version of CF7.