The first Euros match to end goalless since England's stalemate with Scotland 50 games ago, Didier Deschamps's men had the lion's share of the gilt-edged chances, but no Kylian Mbappe meant no killer instinct for Les Bleus.
Meanwhile, Ronald Koeman's men did have the ball in the back of the net in the second period through Xavi Simons, but the Paris Saint-Germain attacker's winner was questionably ruled out for an offside offence against Denzel Dumfries.
The Inter Milan right-back was visibly standing well behind the French defensive wall, albeit not in the sight line of Mike Maignan, whom the VAR room judged was hindered in his ability to dive for Simons's shot by Dumfries's position.
While the stalemate means that both sides are yet to officially confirm their last-16 qualification, they are as good as through to the knockout rounds, while Poland have become the first team to be eliminated from the competition.
With his protective mask in tow - albeit a plain black one rather than the French-patterned one he has been sporting in training - Mbappe took his seat on the France bench, as Marcus Thuram led the line and Aurelien Tchouameni returned to the base of midfield alongside workhorse N'Golo Kante.
Antoine Griezmann rues missed openings in chaotic opening period
Netherlands boss Koeman also saw fit to switch it up in attack, introducing Bayer Leverkusen Bundesliga winner Jeremie Frimpong, who had the first chance of the game with barely a moment gone.
A combination of Theo Hernandez and Maignan managed to thwart Frimpong, whose early opening set the tone for a frenetic start at both ends of the pitch, where both goalkeepers were called into immediate action.
Two promising openings fell the way of the evergreen Griezmann; one from range in the fourth minute which Bart Verbruggen acrobatically tipped over, and another 10 moments later, where he inexplicably failed to sort his feet out from a few yards out after an Adrien Rabiot pull-back.
The latter maybe could have tried to go for goal himself rather than unselfishly laying off his teammate, who was almost punished for his calamity in the 16th minute, but Maignan got down low to beat away a bending Cody Gakpo strike.
The Liverpool man was looking especially dangerous out on the left, but the Dutch were subsequently restricted to counter-attacks as France started to take control of possession, but their lack of attacking X-factor with Mbappe on the bench was evident.
Golden chances were soon at a premium after the fast-paced opening, barring a near-post Thuram strike which sailed over in the 29th minute, but as the half drew to a close, France were increasingly susceptible to sloppiness.
Simons's celebrations soured by contentious offside call
Thankfully for Les Bleus, the Netherlands' final ball often let them down when they strode forward, which is exactly what Thuram did on the hour mark, but his low attempt fizzed wide of Verbruggen's far post as the game entered the last 30 minutes still goalless.
Les Bleus were still looking the more likely to break the deadlock - Tchouameni was the next to go close with a 63rd-minute header which flew just over - two moments before Verbruggen made himself big and denied the luckless Griezmann on the stretch from barely two yards out.
It seemed as if France's profligacy would prove costly in the 69th minute, when Paris Saint-Germain starlet Simons fired in clinically after Maignan had kept out a slick Memphis Depay attempt, but their celebrations were halted by the linesman's flag.
Dumfries was deemed to have been obstructing Maignan from an offside position when Simons pulled the trigger, and following a lengthy check from VAR Stuart Attwell, the on-field decision was upheld.
While Dumfries was not in Maignan's line of vision, the officials had ostensibly judged that he impeded the goalkeeper's attempts to dive for Simons's attempt, and the attacking cavalry was soon called upon by both managers.
The towering Wout Weghorst and Olivier Giroud were sent on for the final 10, in which France still looked the more threatening, but neither team could find the coveted breakthrough.
Man of the Match
While Rabiot's overall midfield performance was dynamic, the Juventus man was far too wasteful in the final third to be considered for this prize, which goes to the omnipresent Kante for the second game running.
Also named the best player of France's success over Austria, the Al-Ittihad man was here, there and everywhere at the Red Bull Arena and even showed some attacking intent with three key passes, including one which should have ended in an assist for Griezmann.
What next for the Netherlands and France?
Level on four points, +1 goal difference and all head-to-head metrics, the Netherlands currently sit top courtesy of their superior overall goals scored, but a point for both on the final day will suffice for qualification.
The Dutch conclude Group D against Austria at the Olympiastadion on Tuesday at 5pm UK time, when France will also pit their wits against eliminated Poland at the Signal Iduna Park.