Sorry, but it's not possible to protect a document with a fingerprint on an Pad, the option is explicitly named "Set Password".
If you thought this would use your fingerprint you were mistaken, however, you had to enter a password, and it's a password only you know.
click here ➜ Password-protect a Pages document on iPad - Apple Support
The other option, is you set "Require Touch ID" for the app. This applies to the App only, not the document that may have been opened at the time. Is that what you did?
click here ➜ Lock or hide an app on iPad - Apple Support
In that case it will usually unlock and open the App with your iPad's passcode as well as Touch ID (or Face ID where available).