Yes, you can download the Eurosport App from your Apple Store directly on your AppleTV.
To stream the Eurosport channels from your AppleTV, you must have registered an account and subscribed to a Eurosport Pass.
Once you have downloaded the App you can make your purchase from the TV.
For more convenience, you might want to consider registering your account and purchase your subscription from a computer. In which case you can access your account by logging in to the Eurosport App on your AppleTV.
If you choose to subscribe from your Mobile App store you will manage your subscription and billing from your Apple or Google App Store directly.
Note: Europsort is also available on your big screen via AirPlay and ChromeCast. The full list of compatible TVs and devices is available here.