If clearing the cookie works, then this is not browser fingerprinting. Browser fingerprinting is about storing information about your browser (screen size, languages enabled, user agent, canvas rendering, and more) you can find whether this information is unique for your browser in https://amiunique.org/
It is illegal in Europe as GDPR doesn’t talk about cookies but about collecting and trakcing user data and granting permission for it. So, if the user refuses the form and you still collect their browser fingerprint, then that’s illegal.