Ellie Downie was denied successive European all-around titles by France's Melanie de Jesus dos Santos, who snatched gold on the final apparatus.
The 19-year-old Briton led Dos Santos going into the floor routine, but her rival produced a dynamic display to finish with a total score of 55.433.
Downie took silver with 55.365 points and Angelina Melnikova of Russia was third with 55.065.
"To come second I'm over the moon," Downie told BBC Sport.
"I was so annoyed not making the floor final so I put everything into today.
"As soon as I managed that last tumble on the floor I was ecstatic."
British Commonwealth all-around bronze medallist Alice Kinsella finished 15th with 50.666.
Earlier, Briton Joe Fraser narrowly missed out on bronze in the men's all-around final. The 20-year-old performed well on the vault, rings and bars to finish fourth with a score of 84.365, just behind third-placed Marios Georgiou of Cyprus, who posted 84.398.
Fraser's compatriot James Hall, who won 2018 Commonwealth silver in the event, finished seventh with 83.097.