Swiss national time trial champion Kung beat Remi Cavagna by 17 seconds, with Victor Campenaerts in third.
Only Cavagna and Campenaerts finished inside a minute of Kung’s time, with Great Britain’s Alex Dowsett coming home fourth, a minute and three seconds off the pace.
Highlights: Stefan Kung wins elite men's time trial at European Championships
Van der Breggen powered to victory in the women’s event, beating defending champion Ellen van Dijk by 30 seconds.
The two Dutchwomen were the standout performers over the 25.6km course in Plouay.
Highlights: Anna van der Breggen powers to win at European Championships individual time trial
Van der Breggen came out flying and caught her minute-woman Marlen Reusser before the first split
Reusser stayed with Van der Breggen to the line and finished 59 seconds behind in third, with Van Dijk coming home in second.