Ester,
We used Alcove and Agape to book our accommodations in Paris. We had a wonderful experience.
You select the area of Paris where you want to stay and the type of accommodation you need. You will see a list of places with a description, the price and a little about your host. Once you've chosen a place, you fill out a questionnaire that describes who you are. Alcove and Agape forwards it, along with your dates of stay, to the host. They then decide if they accept your offer.
If they do, you pay Alcove and Agape a booking fee. When you arrive, you pay your host the remainder in cash. We stayed with a lovely couple who rented out one room in their home. We were a five minute walk from the metro. Our hosts were very gracious and provided fresh pastries for breakfast every morning. We could have eaten by ourselves, but we wanted to spend time with our hosts and we all sat together at their kitchen table and got to know one another. Our room was very comfortable and private, with a sitting room and private bathroom.
From what I can tell, there are different experiences to be had according to your host. If you are adventurous and would like an opportunity to meet a Parisian family, this is just the ticket. If you prefer more traditional accommodations, you'll be better served at a hotel.
Be prepared to fall in love with Paris! We are making tentative plans to return in December. Our oldest grandson will be in Paris for his first semester in college doing a Studies Abroad program. When in high school, he spent six weeks as an exchange student. His family has also hosted two students from France, one who lived with them over the summer. He stays in touch with them. It gives him a chance to keep up his French.