Can I pair my watch with the Withings Health app

It doesn't appear they have an Apple Watch version of their app. Going to the App Store, and you'll find this:

Information

Seller

Withings

Category

Health & Fitness

Compatibility

iPhone

Requires iOS 14.0 or later.

iPad

Requires iPadOS 14.0 or later.

iPod touch

Requires iOS 14.0 or later.

Mac

Requires macOS 11.0 or later and a Mac with Apple M1 chip or later.

As you can see they don't list Apple Watch, so evidently you can't. You should contact them if you'd like to see an Apple Watch version as Apple has no control over their apps.

You're welcome. Not all apps which run on iPhone or other devices are compatible with Apple Watch. This is a 3rd party app, which is not owned by Apple and Apple can't make available for Apple Watch, unless Withings chooses to make the app available for the watch.