The "Ubisoft Game Launcher Error Code 2" typically occurs because of a conflict between the outdated version of the launcher bundled with Far Cry 3
in your Windows settings and uninstall "Ubisoft Connect" or "Ubisoft Game Launcher". Navigate to C:\Program Files (x86)\Ubisoft and delete the Ubisoft Game Launcher folder to clear out corrupted files. Download and install the latest version of Ubisoft Connect
Update Windows: Ensure you have the latest security and feature updates.
If you continue to experience the error after all steps, contact Ubisoft Support and provide your game version (Steam, Epic, DVD), Windows edition, and a screenshot of the error.