https://en.wikipedia.org/wiki/Nuclear_power_phase-out
An immediate effect of this decision was to increase Germany’s reliance on fossil fuels, including “brown coal” which is strip-mined in an extraordinarily environmentally-destructive process. Another effect was to increase the German grid’s reliance on nuclear power generated in France.
Average are misleading.
Solar (photovoltaic) has its maximum around noon, when there is high demand.
The irony is that in summer, it has happened in several warm years now that nuclear power plants in France had to shut down - they are cooled by rivers and when the water level becomes too low, they need to shut off to maintain safety and avoid ecological damage. These are the times when Germany exports most electricity to France.
I think it's exactly the opposite: see [1]. It's a increasingly big problem as more renewable sources are deployed. The peak demand happens at mid-evening and morning hours while, as you said, peak production from renewables is around noon. A possible solution is energy storage but, as far as I now, it's not yet common and not always available depending on the location and type of plant.
Some German articles on the topic:
2012: https://www.heise.de/tp/features/Warten-auf-den-Blackout-in-...
2017: https://www.heise.de/tp/news/Atom-Frankreich-versucht-Blacko...
2019: https://www.heise.de/tp/features/Alle-Jahre-wieder-Frankreic...