Since I looked for this and found an answer not here I will share what worked for me to allow the Note icon from the Action Center to open the Office version of OneNote instead of the free version.
This has been tested on Build 14986.

1. Open Powershell As Admin and run the following command to remove the free OneNote
Get-AppxPackage *OneNote* | Remove-AppxPackage
2. Open the Registry Editor
3. Navigate to Computer\HKEY_CLASSES_ROOT\onenote-cmd
4. Create a new Key named Shell under it
5. Under that, create a new Key named Open
6. Under that, create a new Key named Command
This should look like what the red arrow is pointing to.
7. Modify the (Default) string entry
8. Input the path of OneNote with quotes
This can be obtain easily from HKEY_CLASSES_ROOT\onenote\Shell\Open\Command (the blue arrow).
If you copy the path from this value, do not include /hyperlink "%1"

This should work without any need for a reboot.
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