We stayed at Bernard's place for 6 nights in mid-September (my husband and two kids aged 4.5 and 3 years old). The place is lovely, better than the photos, very clean and comfortable. Bernard and Nicole were very friendly and helped us settle and explained everything about the apartment. Bernard was also quick to respond to my questions prior to arrival.
The weather was very hot but we closed the shutters for the day and that helped to keep it cool, despite no AC. We had everything we needed, in terms of kitchen supplies etc, we only cooked breakfast but there is enough to make a proper dinner etc. The hosts also kindly left some basics for us, tea, coffee etc. The area is lovely, not too touristy but lively, there are numerous grocery shops, bakeries etc, within 2 mins walk from the apartment, as well as cafes and restaurants (too many and hard to choose from!). For the kids there is a big playground 1 min walk from the apartment (and more in the area) and the park Tete d'Or also less than 10 mins walk. The park is fabulous for the kids and has several playgrounds and a zoo (all for free), and also some activities - big 'family' bikes, pedalos, small motorised boats and various ride-on toys, but beware the places that rent them out close on Thursdays and Fridays - at least when we were there - so check on the park's website for opening times to avoid disappointed kids! The other parts of Lyon are easy to get to, approx. 20 min scenic walk to Presqu'Ile or a bit more to the Vieux Lyon, or by metro which is very easy to use (even with two small kids) - there is a metro stop 5 mins walk away.
All in all, a great stay and I would definitely recommend Bernard's apartment for staying in Lyon.