The French qualified less convincingly than initially expected after a 2-2 draw against Portugal in their last group game, having won one of three Group F games.
French left-back Lucas Hernandez had to be pulled out with a knee injury after the first half and remains uncertain against Switzerland.
His replacement Lucas Digne is also healing a hamstring injury and looks unlikely to be in good shape for Monday, forcing potential changes to Deschamps’ defensive plans.
Digne’s replacement in the game against Portugal, midfielder Adrien Rabiot, himself has suffered a persistent ankle injury since the end of the season and is not yet 100%.
To make matters worse, Thomas Lemar injured his leg and Marcus Thuram injured his right thigh in training on Thursday, hobbling the pitch with the support of medical staff.
France are already without Ousmane Dembele after the striker had to be pulled out with injury in his second group game against Hungary. Demebele has been ruled out for the remainder of the tournament and will have to undergo knee surgery.
But despite the injuries, France remains a clear favorite for the game against the Swiss.
Deschamps, who is trying to become the first man to win World Cups and Euros both as a player and a coach, may be struggling with fit defenders but he has won back a striker.
Karim Benzema, who was called up to the national team for the tournament after an absence of almost six years, has scored twice against Portugal.
The French have also never lost to the Swiss in a competitive match. While they are familiar with the later stages of a tournament, their opponents have not reached the quarterfinals of a major tournament in 67 years, since the 1954 World Cup they hosted.
Switzerland qualified as one of the best teams in third place.
“Anything can happen in a tournament,” said Swiss defender Ricardo Rodriguez. “We are fit and ready. We have to be compact in defense and use our few chances. We know the French have a fantastic bench as well. “
“We will give everything. We have already trained on penalties and almost everyone has scored, ”he smiled.
The winners will face the winners of the round of 16 between Spain and Croatia.
(Reporting by Karolos Grohmann; Editing by Frances Kerry)