Henrik Dalsgaard made his third start of the FIFA World Cup as Denmark progressed to the last 16 stage.
France, who knew that a point would be enough to secure top spot in Group C, enjoyed the lion’s share of possession during the opening stages.
Andreas Cornelius got away from his man on 31 minutes and sent a low cross in the direction of Christian Eriksen, but Steve Mandanda was quick off his line to clear away the danger.
Shortly before the interval Ousmane Dembele worked some space on the right but his cross was headed clear by Henrik with Olivier Giroud waiting to pounce.
Henrik was involved at the other end on 55 minutes. Eriksen's 30-yard free-kick bounced off Mandanda and into the path of the Brentford defender, but the France keeper got down to recover.
Thomas Lemar found the side-netting 15 minutes later, before Nabil Fekir tested Kasper Schmeichel with a low, curling effort.
It was by no means a classic – the stalemate in Moscow was the first goalless draw of the tournament – but a point was enough for Denmark to book their place in the last 16. The Danes will face the winners of Group D in the next round.