We stayed 5 days in this apartment with 2 kids (age 3 and 6) at the end of June 2015. This was our first airbnb experience and it was a complete success!
1) Amazing location, very central (2 min from the RER), close to the Luxembourg garden (great playground for kids, also kids can rent a boat to play with on the main fountain), and easy chopping nearby. We could walk to Notre Dame and Ile Saint Louis in 15 minutes. Wine shop, bakery and take out food within seconds of the apartment (Turkish food, Asian fusion, Sushis...).
2) Fabulous apartment. Very bright, very clean, very well organized, very quiet. Lots of room for the kids to play. The apartment was even better than on the pictures. Lovely bathroom and kitchen (modern equipment). Very new and very clean. I am not exaggerating (I am French and I have lived 5 years in Paris so I am well aware of what can be found).
3) Extremely personable owners who went above and beyond what would have been expected. Excellent communication before and during our stay. They went as far as helping us find a nanny. They left some food for us (coffee and juice). They left a lot of room in the closets. They added a bed in the kids bedroom.
The 4 flight of stairs was not too painful, kids never complained about it.
Even my Parisian friends were jealous of this apartment! They told me it was their dream apartment. We will be back!
Note that you can rent strollers and car seats for kids online in Paris (with a very convenient delivery and pick-up option).