If your internet is working fine but Forza Horizon 4 from Steam just won't connect, then please could you try the following as it worked for me!

First, ensure you quit the game, then try following these steps:

1. go to Start Menu > Settings > Gaming > Xbox Networking
2. Click "Fix it", wait for it to finish
3. Click "Check again" and see if Teredo and Xbox Live are now connected. If so...
4. Restart Forza Horizon 4 but DO NOT START PLAYING FROM THE MENU - instead, wait for it to load and click 'SIGN OUT' and confirm you want to restart the game (i.e. once the game has finished showing the opening logos and displays [ENTER] START GAME [X] ACCESSIBILITY, press ENTER once, then go to the fourth option which should be SIGN OUT)
5. Restart FH4 again and sign in. You should now be fully connected.