A 22-year-old climber, also from the Netherlands, was injured in Monday’s accident, regional police of the canton of Valais said.
The 26-year-old Frenchman and the Dutch climber, who was 10 years older, were climbing in two separate rope groups when a slab of rock broke off near the summit overlooking the Trient glacier.
It hit a rope, killing one of the climbers attached while injuring another.
The rock then hit a second rope killing a second mountaineer, police said.
The 3,540-metre Aiguille du Tour, on the border with France, has two summits of equal height at a distance of around 130 metres.
Crossing the south and north of the mountain’s summits is a popular high-altitude feat for climbers.
READ MORE: Why is climbing Mont Blanc so dangerous?
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