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‘Sidewalk’ only makes sense if it's a pavement down the side of a road. For pedestrianised zones it makes even less sense than ‘pavement.’
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My theory is that pedestrianised areas are described as roads, streets or squares. You needn't refer to it as 'sidewalk' or 'pavement'.
Pavement would be better suited though, as it sort of means 'paved area'.