Chris Froome and the other Tour de France leaders laid bouquets on the podium in a solemn ceremony.
There were no kisses, and the usual podium celebrations.
The publicity caravan which precedes the riders and blasts music, rode silently.
A day after the deadly attack in Nice, France's biggest sporting event was in mourning.
U.S. & World
"I'm not as satisfied as I would normally be. Cycling gets a little less important on a day like this," said Tom Dumoulin after winning the 13th stage time trial on Friday.
Froome, second to the Dutch time trial specialist, was in a similar dark mood despite creating bigger gaps on all of his direct rivals with an impressive performance. Froome was the strongest of all the main contenders, and limited his time loss to Dumoulin to 63 seconds.
He lead overall improved to 47 seconds on Dutch rider Bauke Mollema. Fellow Briton Adam Yates was third, 2:45 back. Froome's main rival in the mountains, Colombian climber Nairo Quintana, was lagging by 2:59, and the first alpine stage was not until Sunday.
"Our thoughts are with all the families affected down in Nice. It's where I do most of my training," said Froome, who wore a black armband to his news conference. "It definitely puts things into perspective here."
Amid reinforced security, the race rolled on and thousands of people lined the 37.5-kilometer (23-mile) route in Ardeche to celebrate the Tour and pay homage to the dozens killed and injured by a truck which drove through beachfront crowds celebrating Bastille Day.
There was a minute's silence after the stage, as the yellow, green, and polka-dot jersey holders plus the stage winner gathered on the podium with bouquets.
"It's a very sad day," said Froome, who tweeted a picture of the French flag in the morning.
"I'm affected by all the things that happened in France. My thoughts are with all the families affected by the attack. I want to express my solidarity with France."
Froome attended the post-stage news conference with a black armband. He made only a brief statement after race organizers said he would not take questions about his performance on the bike.
"It's pretty clear today," said Froome, who lives near Nice in Monaco, "everyone's thoughts are with those affected down in Nice, and it's difficult for us to be talking about the race. I do a lot of training on those roads and to see the Promenade (des Anglais) the way it was last night, with bodies all over the place, was just horrific. My deepest sympathies go out to the affected families."
The attack, on France's national holiday, did not deter fans from showing up in numbers at the starting line in the small town of Bourg-Saint-Andeol.
"We can't let our guard down, but it was important that they continued the race," said fan Bruno Pruvost after organizers had an emergency meeting with authorities. "Otherwise, it would be too easy for them."
There was also a moment of silence at the start, several hours' drive from Nice, and Tour director Christian Prudhomme wore a black armband around his blue shirt.
"We want to pay homage to the victims with dignity," said Prudhomme, holding back tears. "We have been asking ourselves if the race should continue and, after consulting with authorities, we have decided that it should. The Tour de France will continue in a subdued and solemn manner."
The publicity caravan, which precedes the riders on the route every day handing out free gifts and souvenirs and blasting loud music, rode silently.
Security had already been reinforced at the Tour this month, with France in a state of emergency since the Paris attacks last November. The three-week race is protected by an unprecedented force of 23,000 police officers, including SWAT-like intervention squads, while security guards perform bag checks and pat downs at the start and finish of every stage.
Eric Luzet, the police liaison officer to the Tour, told The Associated Press that extra security measures were implemented overnight, with 600 police officers overseeing the stage.
Mollema, who was involved in a crash with Froome inside the last kilometer on Mont Ventoux on Thursday, when a TV motorbike was forced to stop on the road because of fan congestion, said his "thoughts are with the people in Nice."
Froome was awarded the same time as Mollema, a decision that left Mollema unhappy. But the Dutch rider put his rivalry with Froome aside, and had a strong ride on the windy and narrow roads in the picturesque Gorges de l'Ardeche. Mollema was 1:54 behind Dumoulin, while Richie Porte, Tejay Van Garderen and Romain Bardet all lost ground to Froome.
Van Garderen sits in sixth place, 3:19 back, with Porte 4:27 behind.
AP Sports Writer Andrew Dampf contributed to this report.