Hi nkjellqvist,
You started from an excellent resource. If you can't make a FaceTime call on your iPhone, iPad, or iPod touch
Specifically checking the connection and testing on a different network the section "If you have connection or sound quality issues with FaceTime" quoted below can help. It also recommend both parties have a known-working connection.
"If your cellular connection or Wi-Fi network are running slow, or other users are streaming audio or video on the same Wi-Fi network, you might have these issues:
- Connection alerts or unable to connect
- Choppy video calls
- Black screen
- Dropped calls
Make sure that both you and the person that you're calling are using a fast Wi-Fi or cellular connection. If you’re using Wi-Fi, FaceTime requires a broadband connection."
Should the issue remain, test a normal restart of your iPhone. Restart your iPhone and review the recommended settings for Wi-Fi routers and access points here: Recommended settings for Wi-Fi routers and access points
Best.