As group winners, France will face the third-place team in either Group C, D or E in Lyon on June 26, while Switzerland will come up against either Germany, Poland or Northern Ireland a day earlier.
It was mission accomplished, therefore, for France, but following narrow wins over Romania and Albania, their failure to record a seventh consecutive victory means they advance with little momentum.
Deployed in his preferred position on the left of a midfield three, Pogba threatened three times in five minutes, forcing Swiss goalkeeper Yann Sommer to produce a wonder save in between two efforts that clipped the bar from outside the box.
He also provided the first half’s only real moment of danger in the French penalty area when he unintentionally scuffed Xherdan Shaqiri’s eighth-minute corner towards his own goal.
The ball struck Swiss centre-back Johan Djourou, sprawled on the French goal-line, and Pogba hacked clear.
Pogba aside, Switzerland’s biggest concern in the first period was the flimsiness of their shirts as Admir Mehmedi, Granit Xhaka and Breel Embolo all had big holes torn in theirs.
Switzerland began to find joy behind French full-backs Bacary Sagna and Patrice Evra in the second half, but the chances continued to fall to France.
Andre-Pierre Gignac shot straight at Sommer, while Pogba excelled again by holding off four opponents and finding Griezmann, who played a one-two with Gignac before seeing a right-foot shot tipped over by Sommer.
Payet made his entrance in the 63rd minute, replacing Kingsley Coman, and received a huge ovation from France’s fans, eager to see greater guile in their team’s attacks.
Payet immediately supplied an injection of dynamism, leaving the crossbar shuddering with a side-foot volley from Moussa Sissoko’s deep cross and then flashing a half-volley wide.
Switzerland have now gone seven games without beating France, since a 2-1 win masterminded by current England coach Roy Hodgson in May 1992, but they will now contest a Euro knockout phase for the first time.
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