After holding the host nation to a 0-0 draw on Sunday, the Swiss secured their country’s first appearance in the knockout stages of the tournament.
Now, they just need to rediscover their scoring touch.
With Albania beating Romania 1-0 in Sunday’s other Group A game, Switzerland finished second behind France with five points after a 1-0 victory over Albania and a 1-1 draw with Romania.
“We are very, very happy,” said goalkeeper Yann Sommer, who produced a superb save to deny striker Antoine Griezmann in the second half.
“We also deserved it in this group. We played well today, we also had some luck. We kept the ball in possession well. For us and for the country, it’s important to be in the last 16.”
Switzerland failed to make it out of the group stage in 1996 and again in 2004, when it lost 3-1 to France.
But perhaps the most painful elimination came in 2008, as the tournament’s co-host with Austria. It lost the opener 1-0 to the Czech Republic and the next game against Turkey 2-1, before bowing out despite a 2-0 victory over Portugal.
Though Switzerland rode its luck on Sunday when shots by Paul Pogba and substitute Dimitri Payet both hit the woodwork, the team’s defense is well organized and Sommer has conceded only one goal in three matches.
The problem is at the other end.
Having been among the top scoring teams in qualifying with 24 goals, its players are suddenly finding it hard to find the net in France.
Despite that, Switzerland coach Vladimir Petkovic sounded positive as he looked ahead.
“We’re through, we can rest up and it’s for other sides to push to play against us,” he said.