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French word étage comes from Old French -age, Old French ester (To be. To stay; to remain.)
-age (Old French)
Forms nouns with the sense of 'action or result of'. Forms nouns with the sense of 'state of being'.
ester (Old French)
To be. To stay; to remain.
étage (French)
(building) floor, storey. (climatology) zone. (geology) stage, division of a geological period. (oceanography) floor in ocean and sea. (rocketry) stage.