Meaning of Rui. French name. In French, the name Rui means-regal.The name Rui originated as an French name. The name Rui is most often used as a boy name or male name.French Name Meaning-regal.Origin-France.Global Star Registery-Name a star after someone special!rench name. In French, the name Rui means-regal.The name Rui originated as an French name. The name Rui is most often used as a boy name or male name. French Name Meaning-regal.