Have just read a Trip Advisor post in the Paris Forum that claims a parent was fined for allowing a two and a half year old to walk through the barrier, rather than use the baggage gates. Apparently the RATP agent claimed this was a breach of safety rules and fined the parent (and child) 60€. Is this just urban legend, or is there really an enforceable protocol, published so visitors can be made aware of it, for child entry. Can parents carry their toddlers instead, where there are no staff to operate the luggage entry gates?
I found the post you mentioned and I don't think it's an urban legend. The mother sounds pretty convincing in her story and I find it believable that such a thing has happened.
I've posted a question to the Paris train authority asking them for clarification. I've read over the rules and regulations and it makes no mention of using the gates / turnstiles in a dangerous manner or allowing children to operate/pass them. I'll write back when I receive a response.
Response from Customer Services at RATP is that children should walk in front of you or in your arms while passing through turnstiles/gates [into a Paris Metro or RER fare-paid area].
Here is the tweet & reply. Obviously this is just a single reply from a service agent and isn't necessarily the position of the RATP overall. But lends evidence that if a rule against bringing your child through a turnstile with you exists, it's not well known.
With that in mind, I think personally it's still easier to use a wheelchair / carriage gate (when available) which are opened via ticket or passes, rather than try to wrangle a child past turnstiles, which are very awkward with the rotating bars and vertical barrier just beyond it (to prevent "jumpers").