Eurosport 1& 2 are among the channels that you can receive with a TVPlayer Plus subscription but they're excluded from the one month free trial period that you usually get when you sign up to the £5.99 per month deal. (If you want them straight away you can contact the company and ask to forego the free period).
You should note that, due to rights restrictions, when using the service via an Amazon Fire TV stick you don't actually get the advertised 77 free channels and 29 subscription channels; you only get 70 free channels and 24 subscription ones because none of the UKTV services are available. (The missing channels are Gold, W, Good Food, Alibi, Eden, Really, Home, Drama, Yesterday, Dave and their associated 'plus 1' channels).