Install the "Sync" app in Cozy. It allows to sync your contacts and calendars through CalDAV and CardDAV.
Then, open the Sync app and go to "Server credentials". You'll find your user name ("me") and a random password there. Use these credentials (not your Cozy username/password) for CalDAV/CardDAV.
Common CalDAV/CardDAV URL: https://yourdomain.cozycloud.cc
User name: me
Password: see Cozy Sync app
Contact group method: groups are per-contacts categories (mapped as labels in Cozy)