There's an article about this in today's Le Parisien (in French): La vraie arnaque des faux sourds-muets.
"Although this type of scam isn't new, it seems to be booming this year in Paris." Apparently there doesn't seem to be much law enforcement can do: few victims file complaints, and the law against aggressive begging doesn't seem to really apply in this case. So far they haven't been able to find the organizers behind the groups of kids.

I saw them "working" in a Carrefour supermarket in Créteil last weekend, so it's not exclusively targeted to visitors at classic tourist sites.