The Euro 2016 hosts secured their place in the knockout phase thanks to substitute Antoine Griezmann's header and Dimitri Payet's fine finish in second-half injury time against Gianni De Biasi's resolute side.
With progress to the last 16 secure, Didier Deschamps could opt to rest some players against a team who have not beaten France since May 1992 and who they thrashed 5-2 at the World Cup two years ago.
But Kante is keen for his side to turn on the style against Switzerland and give fans at the Stade Pierre-Mauroy something to celebrate.
"In the second half we played better, we played more quickly and finally we scored at the end of the game," Kante said. "It was beautiful for the team and a beautiful moment for the fans.
"It was difficult as the opponent wanted to stay in the competition. They needed one point for that and they fought until the end, but we managed to have success in the end."
Admir Mehmedi's strike sealed a point for Switzerland against Romania in their second group game, a result that puts qualification for the last 16 firmly in their hands.
Vladimir Petkovic's side sit second in the group on four points and they are already guaranteed at least third place, though a point would ensure they finish above Romania.
Mehmedi admits it will be a special experience to face the home nation but concedes that his side are looking for vengeance for their World Cup thrashing.
"We have some unfinished business against them," he told UEFA.com. "We know our last match against France wasn't good enough - it's certainly still in the back of our minds - but we're determined to do much better this time.
"It's bound to be a great game and a fantastic experience for us."
Switzerland, who have never reached the knockouts at the European Championships before, had all 23 players take part in training on Friday and are expected to name a full-strength side.
Kante and Olivier Giroud could be left out, with both players a booking away from suspension, while question marks remain over whether Paul Pogba and Griezmann will be restored to the starting line-up.
Key Opta stats:- This will be the 38th meeting between these sides; France have won 16 of the previous 37, with Switzerland winning 12 (D9).- This is the third time France have opened up a Euro campaign with two wins, after 1984 and 2000. They lifted the trophy on these two previous occasions.- France have not had a single shot on target so far before half-time at Euro 2016.- This will be Didier Deschamps' 50th game in charge of France (W30 D8 L11). He's the fifth coach to reach the 50-game barrier with France after Michel Hidalgo, Aime Jacquet, Roger Lemerre and Raymond Domenech.