If CCC is unable to copy your files, then the drive is producing too many errors for any standard macOS utility. Using the command line utility GNU ddrescue to perform a bit for bit clone of the failing drive as suggested by @Tony T1 is the only way to possibly recover the files on that drive except for using a professional data recovery service such as Drive Savers or Ontrack. Both vendors provide free estimates and both are recommended by Apple.
To use ddrescue requires another drive of equal or larger size.
You need to choose wisely which way you attempt to recover your data from a failing drive since you usually only get one chance.
I recommend booting from a Knoppix Linux USB drive since it includes GNU ddrescue and Linux is better able to handle the errors produced by a failing hard drive. You can use the downloaded Knoppix .iso file as a source for Etcher to create the bootable Knoppix USB drive. Option Boot the USB drive and select the orange icon labeled "EFI".
You can also install GNU ddrescue by using Homebrew. If you use macOS to clone the failing drive using ddrescue, then you will first need to "unmount" all volumes on the failing drive. "Unmounting" the drive is different than "ejecting" the drive using the Finder. You will need to use the Terminal app and the command line to "unmount" the drive. Begin typing the following in the Terminal:
diskutil unmount
Then drag & drop the external drive volume from the Finder window to the Terminal window to auto-fill the correct path to the volume of the failing drive. Do this for each mounted volume on the failing drive. You don't need to do this step if booted from a Knoppix Linux drive.
You need to be extremely careful when using GNU ddrescue as it is very easy to make a mistake with the source & destinations for the command. If you make a mistake you may overwrite the data you are trying to recover.
Homebrew:
https://brew.sh/
Install GNU ddrescue using Homebrew:
https://formulae.brew.sh/formula/ddrescue
GNU ddrescue manual:
https://www.gnu.org/software/ddrescue/