I stay here a lot. I just got back from a month in France, 2 weeks and 3 nights of which was spent in Paris. I did 14 nights there over the time - had to stay at another hotel for a few nights because Beaugency was booked.
The Rick Steves 21 Best of Europe tour stays here as well so you've got days where you've got all Americans in the breakfast room. Some days in the breakfast room I've been the only English speaker when a whole group of French business people were staying there for apparently a conference or meeting at a home office or something. By the way...they make just as much noise as a group of Americans, lol!
The furnishings are a bit dated. They use faux suede bedspreads and these have been the same as the first time I stayed there on a 21BOE in 2014. The rooms are small but clean. I did have an issue with the shower in my first room which was the cheapest single they have. The door was one of the triple stack glass doors and it had a lot of mildew build up between the doors. When I checked out the first time I mentioned it to one of the daytime girls at Reception and when I came back a few days later and was placed in the same room some of the mildew had been scrubbed off. TBH, I tried to have a go at it with my fingernail to see if it was permanent and I could not budge it so I feel this bathroom just needs a reno.
The reason I keep coming back is that I really like the staff at reception and the breakfast room. They are the kind of people who recognize their guests after a day or so and usually have your key ready. I travel solo so I want someone on the desk to control who goes in/out of the hotel and these people do. They are helpful and charming.
I like the location. I've had a number of rooms on the front side facing Rue Duvivier and there is some traffic on this street as it's the only thru street in this direction in the area since Rue Cler is restricted travel. There is also some clinking and crowd murmur from Rue Cler in the evening but it just adds to the ambiance for me. I can go to sleep with the windows open without really being disturbed. I also like that there are so many restaurants nearby. I travel solo and if I eat nearby I can have wine with dinner and have a short walk back home safely. Some people find this area "too far" from the center of things but it works for me. I often walk back from the Notre Dame/Louvre area along the river and love the views!
They have AC.
There is an Amorino gelato place nearby (hahaha!!!! Darcy always makes me go here!)
They are excellent at keeping your luggage if you need to drop it early on check in day OR leave it on your departure day. I dropped a notebook this time on my first stay, didn't realize it and they had it waiting for me at check in when I came back. They have a separate luggage room that is in view of the desk or they sometimes stash it behind the desk.
The 2nd hotel I stayed at this time was Hotel Muguet. I liked it a lot and would say it's a step up from the Beaugency. It's also more expensive and Beaugency probably has a better breakfast (altho Muguet might have had a hot egg dish - I'm vegan so just look for fruit and bread.) They had lovely linens, USB ports at the bedside which was so handy for charging electronics, tea kettle in the room, bigger bathroom. My room had a split with the toilet in a separate chamber which doesn't matter at all to a solo traveler but could make a difference to a couple.
I've also stayed at Hotel l'Empereur (sister hotel to Muguet and where some of the Paris and Heart of France departures stay), Hotel Motte-Picquet, Hotel Londres Eiffel, Hotel du Champ de Mars if any are on your list. I've looked at Relais Bosquet which many here recommend but it's so much more expensive than Beaugency.
I selfishly don't jump in to recommend Beaugency a lot mostly because it's hard to get in and I want to be able to stay there! I WILL answer honestly about it!