I took out my first subscription (to Popi) for Dragonfly when she was about 1. She mainly chewed and tore her magazine at the beginning, but we persevered and she grew big enough to engage with the book in less physical ways. We've subscribed to a magazine for her ever since and then added a suitable subscription for Bee when he was old enough. Soon we'll have tried them all!
Bayard has now merged with Milan Jeunesse, so they now have an even more bewildering choice of magazines on offer (see the whole list here: http://www.frenchmagforkids.com/collection_mag.html).
This choice, combined with two imperfectly coordinated subscription sources (my mother and myself!), means that we now have 4 of these magazines landing on our doormat every month! That's on top of the entire back collection of 'J'Aime Lire' books from when we were small ... But I can't complain: the magazines are great. Bee loves his animal magazine Wakou and enjoys seeing how he is now too big for Babar. Both Dragonfly and Bee enjoy Youpi (a Grandma gift). And J'aime Lire is Dragonfly's favourite and one of the main reasons she has managed to transfer most of her reading skills from English to French and can now read in French for pleasure. Hooray!
In addition, much to Bee-the-technology-addict's delight, these subscriptions also come with a web-based subscription to 'BayaM' with games, little films etc. so there is even an interactive element for demanding 21st Century children.
So I'm sure we'll be taking out a subscription for Butterfly when the time comes ...
Do you have any favourite French resources?