For the plums: Put the cranberry juice and sugar into a wide saucepan and stir to help start dissolving the sugar. Then put the saucepan over a low heat until the sugar dissolves entirely.
Halve the plums and remove the pits, then halve them again if they are big brutes.
Once the sugar's dissolved into the red liquid, add the cinnamon stick, then turn the heat up, bring to the boil and let the pan bubble away for a couple of minutes until the mixture is on the way to becoming syrupy.
Now turn the syrup down to a simmer and add the plum halves or quarters and cook them gently for about 10 minutes, although note that this is based on starting off with viciously unripe fruits so you might need less time.
Once the plums are tender but not disintegrating, remove the pan from the heat, cover and leave to keep warm. You can make the plums in advance and either serve them at room temperature with the French toast or warm them up again.
For the French toast: Whisk together the eggs, milk, ground cinnamon and sugar in a pie dish.
Sit 2 pieces of bread in the eggy mixture, turning after each side has soaked up enough to color the bread yellow, so that it absorbs the liquid but doesn't fall to pieces.
Melt half the butter in a frying pan and cook the 2 soaked pieces of bread for a couple of minutes each side. Transfer the yellow, eggy bread, scorched golden in parts, to warm waiting plates. Meanwhile, soak the next 2 slices.
Melt the remaining butter to cook the last 2 slices in the same way.
Serve alongside the beautiful scarlet plum compote.
Make Ahead Note: The compote can be made 1 day ahead. Transfer to bowl to cool, then cover and refrigerate. Warm the compote gently in saucepan before serving.
Freeze Note: Cooled compote can be frozen in airtight container for up to 3 months. Thaw overnight in the refrigerator and reheat as above.