We are returning to Paris over Thanksgiving week with our 16 year old daughter and my parents (in their 70's). We considered an apartment but after reading the comments on this forum and elsewhere, we are now looking for a hotel. It's difficult to find a hotel that can accommodate three in a room - any suggestions beyond the few that Rick mentions in his Paris guide? We'd prefer to stay in the Ile St Louis area or Saint Germain/Luxembourg Garden area.
You don't say what your budget is but if you were interested in a legal apartment, you could look at the Citadines St. Germain. You could get a one-bedroom. The one bedrooms there accommodate 4 people. I guess you and your daughter will be in one room and your parents will be in another. If that is the case, they could get a studio. I just stayed in a triple in Hotel Monge, in the Latin Quarter so not in your preferred areas, which was very nice. The third bed was built into the side of the room and I found the room spacious. We also had the double across the hall. On Ile St. Louis, Hotel Saint Louis en l'Isle has triples and Hotel du Jeu de Paume has a legal two bedroom apartment and a legal 3 bedroom apartment or you could get a double room and a triple room. The triple room that I know of there has a bed and a sofa bed. By the way, Jeu de Paume has spiral staircases that you need to use to access some rooms. I mention that because tight spiral staircases are a deal breaker for me.
By the way, you may get more looks at your question if you post it in the Questions & Answers for France part of the forum. I have no empirical evidence but I feel like you will get more helpful looks there than you will in the section where people go to post reviews.
Look for an apartment with two bedrooms. VRBO is a good rental site. There are others.
If cost is not an issue you should stay at the Luxemborg Parc Hotel. Beautiful, well located, extremely expensive.
The Grand Hotel de Balcons in the 6th arrondissement (near the Odeon) has triple and quad rooms. I've stayed there several times, and would do so again.
We have stayed a number of times at Hotel Le Regent, in the St. Germain area (6th Arr.). They don't advertise, I think, a triple on their website, but they can add a bed to their large double rooms. Though if your daughter is very tall, it might not be comfortable.
We stayed in Hotel Campanile with our family. They had rooms with a double and 2 twins. They are a local chain with locations around Paris. The one we stayed at was in the 11th near Bastille. Very close to 3 metro stops We easily walked to the river and maybe 20 min walk to Notre Dame. It was a modern hotel, not fancy, but clean and quiet.