Hello @essence and welcome to ClassicPress!
Unfortunately, later versions of CF7 require WordPress 5+ and as you may know, ClassicPress is based on WordPress 4.9.
The most recent version of CF7 to be compatible with WP 4.9 is version 5.1.9 which you can download from here https://downloads.wordpress.org/plugin/contact-form-7.5.1.9.zip.
I would suggest the following:
Take a backup of the contact-form-7 folder of your website. Download the above zip file, extract it to a local drive and then replace all files in the contact-form-7 folder with the files just downloaded. This will downgrade your CF7 installation to version 5.1.9 which should work perfectly well with ClassicPress.
An alternative method is to use the WP Rollback plugin.
Let us know if you have any problems.