The British rider remained 52sec ahead of Australian team-mate Richie Porte in the overall standings, with another Australian, Garmin’s Rohan Dennis, a further 2sec adrift.
Europcar’s Voeckler won a sprint finish at the end of the 143km stage raced in bright sunshine, coming through the line ahead of Spain’s Jesus Herrada, Belgian Kevin Seeldrayers and Russian Egor Silin, 46sec ahead of the peloton.
The quartet had kicked ahead of four other riders in a breakaway from the 30km mark, Voeckler’s stage win the first by a French rider on the Dauphine this year.
“That feels really good!” the French champion Voeckler said of his victory — his first of the season after crashing in the Amstel Gold Race on April 14 and breaking a collar bone.
He also fell on his return to competition in the first half of May, taking a tumble on the first stage of the Tour of Belgium and battled to finish the race.
“Nearly everyone tells me that it makes a bad thing good, that I’ll have extra freshness for the Tour de France. It’s possible. But what is certain is that I missed some big races,” the 34-year-old added.
Froome said Sky had achieved their objective for the day.
“An easy stage? No, that’s not the right word for it,” he said.
“The ride was more on the flat than the next two days are going to be but it was a lot more difficult than you would have thought it might be on paper.
“The aim was to control the race and keep the leader’s jersey, but we’re expecting people to attack in the mountains.”
Saturday’s seventh and penultimate stage is a 187.5km ride between Pont-de-Claix and Superdevoluy, passing by Alpe d’Huez and including a descent of the Col de Sarenne, one of the stand-out stages of this summer’s Tour de France for which the Dauphine is a key warm-up.