AccessDeniedException: C:\ProgramData\FAForever\cache\featured_mod\bin\f603e4e8390522eb98ff54f524c001c9

Looks like the client is not able to rename/copy files because of file rights issues. Try uninstalling, then delete C:\ProgramData\FAForever as well, then reinstall.

Maybe you tried to run the client as admin some time ago, that can cause problems