I've not stayed in this hotel which is listed as a 2* hotel. That rating is based on specific criteria. Here's a link that describes what a 2* will have:
https://www.parisdiscoveryguide.com/paris-hotel-star-ratings.html
In June I'd want AC but I am not heat tolerant. 2* hotels usually do not have AC.
There are hotels I like in the neighborhood. I usually stay at Hotel Muguet or Hotel Relais Bosquet. If they are more than your budget, look at Hotel Beaugency on Rue Duvivier. The staff here are very nice, breakfast selections are good. I have stayed here off and on since 2014 but it really needs a complete reno as carpet is stained (or bleached) in places, bathroom doors are scuffed, etc. It's very clean, just needs some updating. I don't normally recommend it any more due to the cosmetic needs but it's more budget friendly than the other 2.