France, who beat Honduras 3-0 in their opening game, top the standings with six points and will advance if Ecuador and Honduras draw later.
Goals within 66 seconds from Olivier Giroud and Blaise Matuidi put France 2-0 up inside the opening 20 minutes at the Fonte Nova arena and on their way to a comfortable triumph on the anniversary of the Knysna bus strike at the last tournament in South Africa.
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The diminutive Mathieu Valbuena scored a third five minutes before halftime after Karim Benzema's 32nd-minute penalty was saved by Diego Benaglio.
But Benzema kept up a rich vein of recent scoring form as he grabbed France’s fourth in the 67th minute and Moussa Sissoko added the fifth.
Substitute Blerim Dzemaili hammered home a low free nine minutes from time and a volley from Granit Xhaka in the 87th minute gave the Swiss a second late consolation goal.
The emphatic win continued France’s World Cup rehabilitation as they seek to bury the ghosts of four years ago when a player revolt left their reputation stained.
Giroud, restored to the starting line-up, rose firmly after 17 minutes to head home Valbuena’s corner for the first goal and from the kickoff, Valon Behrami’s errant pass was picked by Benzema who surged forward to set up Matuidi from the left.
A needless trip on Benzema by Swiss centre back Johan Djourou just past the half-hour mark brought a penalty but Benzema's spot-kick was saved by Benaglio and Yohan Cabaye crashed the follow-up against the crossbar.
Giroud ran deep from his own half on a swift-counter attack to set up Valbuena for the third and France were comfortably in command at halftime.
Paul Pogba’s exquisite pass with the outside of his boot allowed Benzema to turn and score the fourth through the goalkeeper’s legs before the striker turned provider for Sissoko.
Benzema thought he had added a sixth in stoppage-time but the referee blew the final whistle moments before his volley hit the net.
Photograph: Warren Little/Getty Images
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Points Table: Football World Cup 2014