The Juventus midfielder was one of five players brought into the French starting line-up following their 2-0 win over Albania and he had an early effort turned onto the bar by Swiss goalkeeper Yann Sommer.
Pogba then crashed a stunning 25-yard strike onto the crossbar as Switzerland held on at the break.
France are already through to the last 16, but require a point to progress as group winners. Switzerland need a point to be certain of joining France in the next round, but will take over from them as group winners if they prevail.