What I can tell you about the French rule (which you seem to have already observed) is that the generic word (rue, place, boulevard, square, etc.) isn’t capitalised; the specific word is capitalised.
For example: la rue Barbe, le boulevard Iole, la place Rouge.
But some Parisian toponyms are capitalised: le Jardin des Plantes, les Grands Boulevards, le Bois de Boulogne, etc.These are basically places that became proper names.
Hope that helps!