Yes, I believe it's the case. The French nuclear plants can do some load following. But they are not doing it, because it's more inefficient for a nuclear power plants, and as the nuclear is anyway not 100% of the mix, the load following is done by the other parts of the mix that don't have such problem.

On my mind, the main problem of scaling down production for nuclear plant is that a nuclear plant is very expensive, and if it produces only at submaximal capacity, it means that the construction cost is spread on less electricity production.

Operating a nuke at less than 100% is untenable: if run at 50%, each kWh costs twice as much as at 100%, but even running at 100%, it costs radically more than all other choices.