Greg Van Avermaet held on to the yellow jersey he grabbed on Stage 3 and doubled his lead over Geraint Thomas to six seconds by winning an intermediate bonus sprint.
He benefited from a clash of shoulders between Germany's André Greipel and Colombia's Fernando Gaviria in the closing metres, when the former appeared to be on course for a first stage win of this year's race.
On Saturday, Groenewegen had a front row seat for the argy-bargy between Greipel and Gaviria that saw the duo demoted after the stage.
"It is very emotional, I went through such a hard period so today is pure happiness", said Degenkolb, who suffered several fractures and a serious finger injury after he and some team mates were hit by a vehicle during a training ride in January 2016.
But after losing his second teammate within the space of a week, Bardet knows his chances of keeping pace with Froome and his Welsh teammate Geraint Thomas over the coming days will be fully tested.
The German, who won the Queen of the Classics in 2015, was one of three riders to jump away from the main pack 19km from the line and he was the fastest in the final sprint, beating overall race leader Greg van Avermaet of Belgium.
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The mostly flat 181-kilometer (112-mile) ride from Dreux to Amiens comes before the three-week race faces one of its most hard legs when it hits the tricky and occasionally treacherous cobblestones.
Mitchelton-Scott's Adam Yates and Sky's Chris Froome remain 13th and 14th, with their deficit to yellow growing to 65 seconds. Van Avermaet said. "But everyone kind of enjoyed it - the first day we could really relax".
The riders now face a long transfer to Annecy, but have Monday's rest day to recover before the race moves into the Alps and the battle for overall victory hots up.
"This is where it gets hard, as we hit the first mountain stage", Wiggins said. The result was another mostly calm ride. UAE Emirates leader Daniel Martin, the victor of Stage 6, bloodied his left elbow and tore the back of his shirt.
Martin and 11 other riders couldn't reconnect and Martin lost more than a minute, falling from 21st to 31st place at 2:47 behind.