Here's how to use your Apple TV Remote for Apple TV 4K or Apple TV (4th generation) to navigate through the Zattoo app:
Switching channels: Swipe left or right to switch channels or open the channel list by swiping up on Touch surface and then select Favorites / All channels / Categories.
Open channel list: In Live TV > Swipe up on Touch surface then select Favorites / All channels / Categories.
Pause/Resume: Play/Pause button on remote control or press to click on Touch surface.
Go forward/Go back: press to click on Touch surface, then swipe to right or left.
Subtitles: Swipe down > Subtitle > select
Change audio track: Swipe down > Audio > select
Restart/Replay: Swipe down > Info & controls > Replay
Go step back: Press Menu button to go back to the step before.
Recording options: Swipe Down > Info & controls > Recording Options
Open details from the player: Swipe down > Info & controls > Details
Volume: Press +/- button.
Open Menu: Press Menu button.
Close app: Press Apple TV App/Home button.
You can also use the Apple TV Remote app to navigate through the Zattoo app with touch gestures. Navigation is identical except for zapping through the tap gesture. For channel switching, open the channel list by swiping up and then select channel.