Romania came close to frustrating France in the tournament-opening match before Dimitri Payet's sublime winner gave the French a last-gasp 2-1 win.
The Swiss meanwhile had to fight before Fabien Schaer's forceful header secured a 1-0 win over 10-man Albania.
Schaer, the 1.86 metre (6ft 3in) Hoffenheim defender, makes a habit of scoring for the national side -- his decisive goal on Saturday was his sixth in 21 appearances.
Victory at Parc des Princes would almost certainly guarantee Switzerland a ticket for the round of 16 from Group A -- and they will not want to be facing France in Lille on Sunday after a defeat to the Romanians.
"We watched France against Romania, and Romania matched them for the majority of the game," he said.
"We know we'll have to up our game to beat them."
Goalkeeper Yann Sommer urged his teammates to throw caution to the wind. "One point will not be enough for us to qualify," he said.
Romania's Nicolae Stanciu said although his team have fewer players in Europe's top leagues, they were a match for the Swiss.
"I think we are at the same level," the talented Steaua Bucharest midfielder said.
"They will remain unique and it will take time to achieve what they achieved," he said.
The Romanians received glowing praise from their usually critical national press for their performance against France and the atmosphere in the camp is relaxed after they enjoyed a barbecue with their families in the team hotel on Monday.
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