I generally watch the free highlights, but I've been looking into the paid services.
Between Peacock and skiandsnowboardlive.com, they should have most of the FIS world cup events. This schedule shows only through the end of December, but it is representative of what is on each of these channels:
https://olympics.nbcsports.com/2022/12/19/alpine-skiing-world-cup-tv-live-stream-schedule-peacock/. Of course, neither one has every FIS alpine ski event.
Peacock is $4.99 per month, or $9.99 per month without ads.
skiandsnowboardlive.com has the following pricing:
Standard pricing for streaming service
All-Access Monthly Pass for $15.99
Discipline Monthly Pass for $8.99
Pay-Per-View for $1.99
Free highlights
If you want to watch on Eurosport, that is not an option in the US due to geo-restriction of the content. Unless you want to get fancy and use a Europe-based VPN address.