Just downgraded from iOS 11 beta to iOS 10 and now I can't pair my Apple Watch
You can’t downgrade watchOS, no matter which version of iOS you're running on the paired iPhone. If you want to keep using your iPhone with your WATCH you have the following options:


Reinstall the corresponding beta version of iOS (11 for watchOS 4, or 10.3.3 for watchOS 3.2.3).
Wait for the public release of the required version of iOS (10.3.3 should land the week of July 17th).
Take your WATCH to an Apple Store so they can downgrade it for you. This requires them sending your Watch in for service, which will take a few days.