Even if that were an option -- to where would I ship it? If I was staying at a hotel overnight, I'd be able to leave the bags there (or at least I'd expect to check them there). Since I'm not "parked" anyplace, I don't think that would work.

Long ago, when I was growing up in New York, I remember that all the big museums had check rooms. (If nothing else, people needed to leave coats and raingear.) I wonder if I could do so in Paris as well?