Having survived a physical Honduras side in their Group E opener, Didier Deschamps' men faced a seemingly more difficult task in Salvador, but they ran roughshod in an exhilarating display that left Ottmar Hitzfeld's men shell-shocked.
Olivier Giroud, Blaise Matuidi and Mathieu Valbuena were all on target in a breathless opening 45 minutes in which Karim Benzema missed a penalty.
He made amends with his third goal of the tournament in the second half, before applying the assist for Moussa Sissoko to make it five.
Switzerland - who beat Ecuador 2-1 in their first pool match - were stunned by two goals in as many first-half minutes, first Giroud crashing a header past Diego Benaglio, before the goalkeeper was beaten easily by Matuidi's shot.
Granit Xhaka had a goal ruled out for Switzerland, before Benzema - who notched a brace against Honduras - saw Benaglio save his spot-kick.
It made little difference as Valbuena capped of a wonderful counter-attack in the 40th minute to effectively end the contest by half-time.
Benzema's close-range strike and a Sissoko effort added further gloss in the second period, before Blerim Dzemaili and Xhaka bagged late consolations.
France are now on the brink of the last 16 having taken a maximum six points, while Switzerland still have work to do in their final pool encounter with Honduras.
Switerland's woes started early when Steve von Bergen caught a boot in the face from Giroud and had to be replaced.
And Giroud was in the thick of the action again when he put France ahead in the 17th minute.
The Arsenal striker leapt highest to thump Valbuena's corner past Benaglio who, despite getting a full hand to the ball, could not keep the effort out.
Just a minute later France took complete control.
Benzema pounced on Valon Behrami's poor pass before playing in Matuidi on the left of the box and he side-footed past Benaglio at the near-post, the goalkeeper perhaps beaten too easily.
France were handed a reprieve when Xhaka turned home Gokhan Inler's mishit shot, only to be denied by the offside flag.
Having escaped, Les Bleus missed the chance to extend the lead in the 33rd minute when referee Bjorn Kuipers pointed to the spot after Johan Djourou recklessly felled Benzema.
However, Benaglio dived to his right to keep out the Real Madrid striker's spot-kick before Yohan Cabaye inexplicably volleyed the rebound against the crossbar.
But France did get a third just five minutes before the break.
Raphael Varane brought the ball away following a Swiss corner before producing an exquisite pass that sent Giroud free down the left and he in turn laid the ball across goal for Valbuena, who could not miss from inside the six-yard box.
Switzerland showed more intent after the break, but were restricted to long shots.
Despite the improvement, France had a fourth when substitute Paul Pogba's fine ball with the outside of his boot was swept home by Benzema, Philippe Senderos not helping his side with a poor attempted clearance.
France made it five just six minutes later, Benzema once again involved as he laid on for Sissoko to drill home from the right side of the box.
Dzemaili pulled a goal back with a low 30-yard strike in the 81st minute, before Xhaka added further respectability to the scores when he met Gokhan Inler's chipped pass with a superb guided volley, but it was too little too late.
Benzema was denied a stunning late sixth as the whistle had gone before his first-time strike from the edge of the box had hit the back of the net, much to the Real Madrid forward's annoyance.
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