Paris Hotesl for PD patient

Nelson, I think the first place I'd enquire is through the Rick Steves Trip Planning department:

https://www.ricksteves.com/travel-help/plan-your-trip-with-our-expert-consultants/
It would certainly be worth it to get accurate information for your situation.
Best of luck!

I don't think that a hotel would - or could - take responsibility for your medical needs.
There is a question of the hotel's insurance, and they would have to open the boxes of solution, which would probably contaminate them. They would probably refuse them, and not return them to where you live.

If possible, I would suggest putting your boxes of solution in a checked bag - if it won't fit in a cabin sized bag. It would be worth the $50 or so to have them there when you need them.

I know nothing about peritoneal dialysis so I have to ask if the solution must be kept refrigerated and also how large is the box or boxes that you will need for 10 days? I have shipped many things to my hotels and never had a problem with the hotels agreeing to hold them and deliver them to my room upon arrival but none of the items were medical supplies so I don't know if my experiences will predict what will happen for you. I think that a hotel would accept delivery if there was no storage issue and no need for them to refrigerate the items, but i could be wrong. That being said and not knowing your budget, try the Signature Saint Germain, Hotel Odeon Saint Germain, Hotel d'Aubusson, Hotel Londres et Eiffel or Hotel Monge. I have stayed at each of these places and had packages delivered there and held for me in anticipation of my arrival without any issues but again stressing that these were not medical supplies or in any way fragile items and also not especially large packages. As an alternative, is it possible to bring a few with you and buy the solution in Paris. See http://www.auraparis.org/en/what-we-do/our-health-offers/peritoneal-dialysis

You will have to schedule an appointment with a major hospital to obtain what you need, which will probably tie up your plans somewhat. The solution is not refrigerated.
http://www.auraparis.org/en/activities/patients-staying-temporarily-in-paris-and-the-ile-de-france-region

The fluid would be very difficult to pack in a checked bag, which is probably why the OP has plans to ship it. Dialysis companies are accustomed to this sort of arrangement. I think all you can do is pick a hotel you like based on price and location and contact them about their willingness to store your supplies. I would check with your dialysis company to get approximate sizes and weights for the boxes you will ship so you can provide the hotel with that information. I would think most hotels would be willing to help, just make sure to call them before you leave home to make sure they have arrived. The hotel wouldn't be taking responsibility for his medical needs, they would just be accepting a delivery. To me this would be no more liability than a hotel that offers to store a traveler's insulin in a refrigerator for them. The customer does all of the dialysis independently and wouldn't need any assistance or accommodations for that. But perhaps in the business world it is more complicated than that.

I think your best option would be to contact the hotel(s) you are interested in and ask if they can hold for a day or two, x'' number of boxes of whatever size box it is. None of us here are likely to know just how much solution you require for 10 days and what volume of space that it occupies.

Is it something that can be stored in your room or are you expecting the hotel to have a storage space for it?

I agree with Tamara. I think most hotels would be willing to hold the package. I also think this is very likely to be true at smaller places but I bet you the Hotel Le Bristol or the Ritz or the Peninsula concierge would also accept the package. I forgot to include Le Bristol as a place that has accepted packages in the past in my earlier post. And same for Hotel Chavanel and Hotel Edouard VII. The Signature Saint Germain and the Hotel Londres et Eiffel and the Hotel Apollon Montparnasse are owned and managed by a very warm and kind family. I don't know for sure but they do not seem like the type that would say no unless their insurance forbids it. I think you should be sure to have the name of the person who has agreed to accept the package, confirm that the items are there before you head to France, and bring enough for a day or two if possible in case something goes wrong (wrong stuff shipped, somehow the items was lost between confirmation and your arrival, or as has happened to me once, the item is stored somewhere but only one person knows where and arrival day is her day off).

I think shipping this many boxes of solution would be prohibitively expensive.
The concierge of the Ritz or the Peninsula hotels might accept them, but I would think the OP is looking for a moderately-priced hotel, which might not have a concierge.
If you haven't booked the room for the first or even second day, I doubt this will be possible, because you haven't even paid for the room, yet.

Holding a package for guest arrival is common and uneventful at larger hotels that have conference or event room space for business travelers. The down side is that many hotels will charge an extra fee for this service.

How many fluid ounces in a package, and how much do you need daily?

If it's commonly used in France, could you have it delivered from a local company? Or will it have to be shipped from US?

Congratulations on your travel plans! My niece recently took her first trip with PD (Mexico) and was excited to be able to travel.
Assume you have discussed with your nephrologist about finding a backup medical facility in Paris (and carrying your medical records) in case you need assistance/checkup. One information source is
Livenow.info

I already mentioned that if the OP wants to avoid having packages delivered, he would have to make an appointment at a dialysis center.

Hopefully, they can provide him with the solution he needs, but he will need a French doctor's prescription for the whole 10 days, then go to the pharmacie.