I subscribed to the Apple One family plan and downloaded Apple Music, but it says to pay for the plan.

Thanks for reaching out 수아161,

We understand that you’re part of a Family Sharing group but are unable to access Apple Music through the Apple One family subscription. 

Let's see if we can narrow down why this might be happening. Go ahead and try these steps first, and be sure to test after each step:

• Restart your iPhone
• Confirm that the Family Organizer has the subscription shared with you, and sign out and back in to Settings > Media & Purchases. (If you already have an Apple Music membership, signing out will remove all offline music). 
• Share Apple and App Store subscriptions with family members on iPhone.
• If you can't find your family's shared content.

Hope that helps.

Take care.