Wpa-enterprise, connection on client, not on access point

It doesn't matter. From your PC that is connected on the LAN port you'll open a browser and try to open a page. Any page, shouldn't matter. The captive portal will redirect your browser to a login page where you'll click accept, or login with user/pass.
After you authenticate there, you will be able to access the internet. However this needs to be done using the DNS provided by Eduroam.