How can I access built-in music in Final Cut Pro?

As Tom an Ian pointed out, in your screen shot, you're looking at the Apple Music library, which shows what you've collected there. That has nothing to do with the FCP/iMovie "additional content." All of that "additional content" that comes with FCP/iMovie is found under "Sound Effects." Your "jazzyfrenchy" has nothing to do with FCP or iMovie content. AND, be very aware, when you click on Sound Effect, it may take a really good hot minute or two before you see anything appear. It's kind of slow to load up.

FCP has no music of itself, only effects. However, if you have iMovie installed, FCP will include the iMovie jingles in the Audio and Music browser.

The tunes in the screenshot you posted have never been part of FCP or iMovie. They must be something you have imported.

If you want to copy the iMovie sound effects/jingles go to the iMovie app in the Applications folder.

Right-click (Control-click) it and select Show Package Contents/Contents/Resources/iLife Sound Effects.

Hold down the Option key as you drag the iLife Sound Effects folder to your desktop and it will create a copy leaving the original untouched.

At the same time you could also copy the iMovie Sound Effects and iMovie Theme Music folders.

That Music folder is the content of your Music library. You may have put jazzy french into Music.

The content that comes from iMovie is in Sound Effects categorized as Jingles

In iMovie they are also listed as Jingles under Sound Effects.

Not sure if it would help, but since it's a mystery, go to the Final Cut Pro menu, choose "Download Additional Content" and see if that helps. I'd also move iMovie to the trash, then go to the App Store and re-download it from scratch. Another option would be to go to macOS System Settings, to Privacy & Security, and verity FCP has full disk access.

David Sommers wrote:

Where would I find it to reconnect it?

If you download iMovie it should appear in FCPro automatically.

Otherwise it can be done manually through Package Contents.

Al

Does built-in music mean sound effects? Or is it your personal music files?

Please show me a screenshot.