After booting up my first germany game in 1.5.3 Waking the Tiger i conquered France but since Italy somehow took most of France even though Italy didn't do anything I formed Vichy France. Later there is the Case Anton which says it will let me annex Vichy France and possibly steal its navy. When I enacted however, nothing happened. Is this supposed to happen? Also why did Italy get most of France as if it was the one who capitulated France when it was actually me who got the capital?
You have to wait a bit. If you arrive in Toulon with 48 hours (just strat deploy a motorised division there) you need to wait about 10 days for an event that tells you if you successfully seized the Vichy fleet or not. If it's against the AI you should get the entire fleet.
Sometimes the fleet spawns outside the Mediterranean at Casablanca (IIRC) though, so if this happens I just use the console to teleport the fleet back inside the Mediterranean.
Also, Vichy will call your allies to war while you're waiting in that 10-day period after arriving in Toulon. So keep Italy, Hungary and Bulgaria out of the Axis until you've annexed Vichy if you don't want them to join (yet).
EDIT: does anyone know what options/decisions France and UK get if Germany takes Case Anton? How are they able to respond?