There are two common approaches to that problem.
1) You can use the web server and|or the OS authentication and authorization mechinisms. The would normally require to not allow 'anomyous' login, but use one of the authentication methods supported by your web server of choice. Then the web server should be able to tell the OS who the user is and the OS can use that against the authoization data set on the files and or directories to see if that user is allows to access that file.
2) You can relocate the files to a directory that is outside the web root. In this case you would not offer links directly to the files themselves. Rather you would have links to a file delivery CFML code. This code would see what file is desired from the data in the link. It would fetch the file with <cffile...> functionality and the deliver the file with <cfcontent....> functionality. This solution allows all the authentication and authoization logic to reside in the CFML code base rather then invoking other technologies.