The French backed up their opening 3-0 win over Honduras by racing into a 2-0 lead as Olivier Giroud's 16th-minute header was followed by Blaise Matuidi's goal just 66 seconds later.
Diminutive right-winger Mathieu Valbuena put the result beyond doubt with France's third just before the break. Real Madrid's Karim Benzema missed a first-half penalty, but then netted their fourth before Newcastle United's midfielder Moussa Sissoko also claimed a second-half goal.
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The Swiss, who have not beaten France since 1992, may now need to beat Honduras next Wednesday to qualify for the last 16. They beat Ecuador 2-1 in their opener.
On the anniversary of their infamous strike at South Africa 2010, France put themselves amongst the World Cup favourites.
Salvador has now seen 17 goals in three World Cup matches -- the most by far of Brazil's 12 venues -- after the Netherlands routed Spain 5-1 here and Germany hammered Portugal 4-0 last Monday.
Swiss coach Ottmar Hitzfeld was forced into an early change when centre-back Steven von Bergen had to leave the field with a heavy cut over his left eye, Philippe Senderos replacing him.
Giroud, back in for Antoine Griezmann after spending most of the Honduras win on the bench, wasted little time in repaying Deschamps' faith for the opening goal.
He met Valbuena's floated corner and his looping header beat Benaglio despite the goalkeeper getting an outstretched glove ot the ball.
It was France's 100th goal at World Cup finals. The French doubled their lead 66 seconds later as Benzema snapped up a stray pass, charged into the Swiss half and put away Paris Saint-Germain midfielder Matuidi, who fired inside Benaglio's near post.
The Swiss came perilously close to pulling a goal back as a Xhaka strike was ruled offside, then Xherdan Shaqiri's shot flew across the French goal.
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