Slovakian Peter Sagan was second and France's Tony Gallopin finished third. Italian Vincenzo Nibali retained the overall leader's yellow jersey. It was a moment to savour for the OPQS team after their British sprinter Mark Cavendish pulled out injured after a crash on the first stage.
"I am very happy to have won this after the hard luck we had for the last six days and especially Mark Cavendish's crash," said Trentin after the 234.5-km ride from Epernay.
"We came to the Tour for Mark to take the yellow jersey in his mother's home town and it ended in a crash. The next morning, he gave us a very good speech, telling us that we should win a stage, that we could do it. We did it at last."
Van Garderen, 11th in the race at the start, fell with about 15 kilometres to go and lost 1:03 to the other favourites, dropping to 18th overall. Also involved in the crash was his Colombian BMC team mate Darwin Atapuma, who abandoned the race because of "unspecified injuries", the team said.
"(It is) Nothing major, I'll be definitely fine to start tomorrow. It's a tough blow but the Tour is long, the race changes," Van Garderen said. "It's definitely not a good day for the team. Atapuma, we were keeping him fresh for the mountains and to lose him is tough. He banged his knee pretty hard."
In the final straight Garmin-Sharp rider Talansky fell after colliding with Australian Simon Gerrans.
He got back on his bike and, as the incident happened inside the final three kilometres, was credited with the same time as the bunch.
He moved up to eighth overall, but was fuming at Gerrans, who apologised shortly afterwards.
"Gerrans moved right over onto Andrew's front wheel as Andrew was trying to get out of the way," Garmin-Sharp manager Jonathan Vaughters told reporters.
"Not much you can do about that. He's fine...
"First thing he said to me was 'I want an apology from Simon Gerrans'. That means he is doing fine, He's going to be a little bit stiff tomorrow but he is alright."
The sprinters dropped out when the peloton reached Col de Maron, a short fourth-category climb 20 kilometres from the finish.
In the final kick, a 1.3-km climb at an average gradient of 7.9 percent, Sagan and Greg Van Avermaet powered away from the pack before being caught.
Sagan was then beaten by a tyre's length by Trentin who also won a Tour stage in Lyon last year.
"For a while I did not know if I had won it," said Trentin.
The Tour hits the mountains on Saturday as the eighth stage takes the peloton to the Vosges massif for a 161-km trek from Tomblaine to Gerardmer.
(Reporting by Toby Davis; editing by xxx)
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