You cannot plug a GameCube controller directly into a Wii model RVL-101. This launch model lacks the GameCube controller ports and memory card slots found on later revisions (RVL-001).
Adapters are widely available on Amazon, eBay, and retro gaming shops ($15–$30). The official Wii U adapter works perfectly on Wii via homebrew (Nintendont).
Note: This applies to the original RVL-101 (2006 launch model). Later RVL-001 models do have built-in GameCube ports.