"Remember," in French, is a reflexive verb, "se souvenir" -- there's *always* a pronoun before the verb. No matter who is remembering or what they are remembering. "I remember you" would be "Je me souviens de toi." So there really isn't much significance to the presence of a "me" in the slogan. (This writeup was done as a correction to the earlier writeup's interpretation of the pronoun "me" being present -- I'm leaving it up for now as a French grammar lesson.)