No, I don't think we need both. In particular, building new nuclear plants would be worse than just putting all that money into renewables + storage. The latter displaces fossil fuels more quickly and more cheaply.
Parts of Europe are close to the worst case for renewables (specifically, some parts away from coasts without a good wind resource). Even there, new nuclear might be only competitive with renewables.
This web site provides an optimization scheme for determining how expensive it would be to provide 365/24/7 steady power from wind/solar in various geographical areas, using historical weather data. Even in Europe it's not that bad. The 2030 cost figures may already be obsolete given the crash in battery prices.
Note that in this model it's essential to have something beyond batteries to use for long term storage (to smooth wind output, and to provide seasonal storage of solar output). The model uses hydrogen, but long term thermal storage may be even cheaper. Europe has ample geology for storage of hydrogen (salt formations).
I don't think anyone is arguing nuclear instead of solar. It's both. We need both.