After three failed attempts to advance from the group stage, Switzerland can reach uncharted territory at the Parc des Princes if they beat Romania.
"The first game [a 1-0 victory over Albania] gave us confidence. The team is very relaxed. They won their first battle and there are still two battles to fight, the second of which is tomorrow," said defender Johan Djourou.
Defeat for Romania would leave their qualification hopes hanging by a thread.
France can also clinch a spot in the knockout phase, but it won't be straightforward, players say.
Dimitri Payet's stunning 89th-minute strike steered France to a 2-1 victory over Romania to kick off the competition on Friday, but midfielder Blaise Matuidi knows newcomers Albania cannot be underestimated.
"They're a team we know well. They're a team we haven't had good results against recently," Matuidi told UEFA.com, with France held 1-1 by Albania in November 2014 before suffering a 1-0 away defeat almost exactly a year ago.
"It's not going to be an easy match. We saw against the Swiss even with 10 men they had their chances," he added, as Albania seek their first points after an opening 1-0 loss to Switzerland on Saturday.
"I think the fact we picked up three points (against Romania) will liberate us a bit."
However, France will be hoping for an improved performance from midfielder Paul Pogba -- tipped to be one of the stars of the tournament -- after a disappointing display against Romania.
Pogba was benched for France's second game at the 2014 World Cup, but coach Didier Deschamps refused to answer whether that would again be the case at the Stade Velodrome.