Can't connect my Jaybird X3 Wireless Headphones to my new Apple Watch Series 3

If you have not done so yet, try a hard reset on your Apple Watch and see if it will then "See" the Headphones.

To hard reset an Apple Watch:

1. Remove the Apple Watch from your wrist. (This is optional, but I recommend it.)
2. Press and hold the Digital Crown and side button simultaneously.
3. Hold until your screen is off and let go when you see an Apple logo.

Use Bluetooth accessories with Apple Watch - Apple Support

Found this and it might be helpful...

How to pair your Apple Watch with wireless headphones or a headset

1. Put your headphones or headset into Bluetooth or W-series pairing mode. ...
2. Press the Digital Crown to go to your Apple Watch's Home screen.
3. Tap the Settings app.
4. Tap Bluetooth.
5. Tap the name of the device you want to pair with.