If this didn’t work, you can also try to clear cache and data of the Google Play services and Download Manager app. If there’s little free space left, please delete unnecessary files and remove seldom used apps to free up space. So you should go to check how much free space is left. The second thing to do when your Google Play won't update apps is to check the internet connection on your device.
When you can't download apps from Play Store, you should first restarting your device and try the download again. Restarting is an easy but effective method to solve many system related and app problems.