There should have been no way for a double charge to occur.
If you were subscribed to Apple TV before this the new option will have cancelled the active Apple TV subscription automatically and offer a prorated refund.
From iCloud+ with Apple TV and Apple Arcade - Apple.com
If you currently subscribe to Apple TV or Apple Arcade individually but not iCloud+, you’ll be notified via push notification and email that you’re now subscribed to iCloud+, and you’ll continue to have uninterrupted access to Apple TV and Apple Arcade through your new iCloud+ subscription. Your existing individual Apple TV or Apple Arcade subscription will be cancelled as it’s no longer needed. On Arcade, your game progress and saves are preserved, and there’s no interruption to your access.
If you were in fact double charged and have not received a refund, log in to https://reportaproblem.apple.com with your Apple Account and find the charge you wish to contest and click on Request a Refund.
click here ➜ Request a refund for apps or content that you bought from Apple - Apple Support