1. Preheat the oven to 180 °C (350 °F).
2. Wash the plums and Reine-Claude plums. If the skin of the plums is too bitter, peel them.
3. Pit the fruits and cut them into small pieces.
4. Melt the butter gently.
5. Meanwhile, whisk the eggs and sugar by hand until the mixture is frothy and slightly increased in volume.
6. Gradually add the flour, then the melted butter, mixing well.
7. Stir in the baking powder, cinnamon, black plums, and Reine-Claude plums.
8. Grease and flour a loaf pan (or use a non-stick pan to avoid having to add butter and flour), and pour in the batter.
9. Bake in the oven for 50 minutes at 180 °C (350 °F).
10. If the cake becomes too brown during the last 15 minutes, cover the dish with aluminum foil.
11. Check the doneness of the cake with the blade of a knife, it should come out clean.
12. Allow the cake to cool before removing it from the pan.