Hello achrisvet,
Thank you for using Apple Support Communities. It's my understanding that you're unable to successfully download your Apple Watch update due to a Wi-Fi connection error. You've come to the right place! I'm happy to help.
I recommend testing the issue on another Wi-Fi network. If the issue persists, restart your Apple Watch and iPhone. Restarting can resolve many unexpected behaviors.
How to restart your Apple Watch
Restart your iPhone, iPad, or iPod touch
If the download continues to pause, open the Apple Watch app on your iPhone, tap General > Usage > Software Update, then delete the update file. After you delete the file, try to download and install the update again.
Let us know the results. Please include any other error messages and additional troubleshooting steps you may have tried.
Have a wonderful day!