Denmark's Thomas Delaney hobbled off after a strong challenge and was replaced by Lukas Lerager as the game drew to a close with boos from the neutral spectators in Moscow.
Denmark - likely to face Croatia next - rarely threatened and appeared happy with a 0-0 draw that sends them into the knockout stages for the first time since 2002, with Tottenham star Christian Eriksen providing their greatest threat in front of goal. "We were actually expecting a nice game".
In its first match of group play, Denmark handed Peru a 1-0 loss to pick up three points. "It is hard to say if we will play with a more open style against Argentina - how we play will depend on the opposition".
Steve Mandanda became France's oldest World Cup debutant and the goalkeeper nearly cost his side, spilling a long-range Eriksen free-kick before recovering to claim the loose ball ahead of lurking striker Andreas Cornelius.
"We did what we had to do, and we got the result we came to get", Dalsgaard said.
Yussuf Poulsen was suspended against France after picking up his second yellow card of the tournament against Australia.
Australia will be chasing a slim chance of making the World Cup last 16 when they take on Peru. Russian fans broke into their national chant several times to break the boredom.
It was the longest a World Cup had gone without a goalless draw since 1954, a tournament of 26 games which all delivered at least one goal.
The second half was a slight improvement on the opening 45 minutes, with substitute Nabil Fekir finally showing some positivity. They met a solid Danish defence content with the draw.
France has won Group C and will open the round 16 on Saturday afternoon in Kazan, playing the Group D runner-up.
Denmark gets an extra day off and plays the Group D victor, likely Croatia, on Sunday evening in Nizhny Novgorod.
All four group D teams are still in contention: Croatia, Nigeria, Iceland and Argentina but only Croatia and Nigeria can win the group.