The Liverpool athlete, Britain's only ever world gymnastics champion, won the bars title on 2006 but was unable to defend her title last year because of injury.
However, she was delighted with her success in the floor event.
"I was a late entrant into the competition because I've had injuries and I only started working on my floor routine two weeks ago," she said.
"It's always nice go home with a medal, whether it's on the bars or on the floor. It's nice to show I'm still up there on the floor and people can watch out for me later in the year at the Olympics."
Replay: Tweddle's floor and uneven bars routines in France
Rebecca Downie came eighth in the uneven bars and the vault while Britain came sixth in the team event final.
The British squad, which had been battling a bout of flu, also included Laura Jones, Hannah Clowes and Marissa King.
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Beth Tweddle's uneven bars guide
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