I think that on the whole ( am generalising, obviously cannot speak for every french or english parent!), the French are much "stricter" with their children and children learn to conform and "be civilised" young. An insult here is "mal élevé", which means badly brought up, and manners really do count. Children learn to sit at table, to greet strangers with a kiss, to say good bye and look the person in the eye - very early on. There are no exceptions. Where an English parent would smile with amused exasperation at a child shredding her bread into crumbs and chucking it on the floor (seen a couple of weeks ago in a restaurant), this behaviour would not be tolerated by a manners conscious French parent.
I have seen parents wallop children here and no one bat an eye. Physical chastisement is common, obviously battering is not acceptable, but smacking setems to be.
When my ds was 2 and a half and in maternelle (nursery), his older sister at the same school was sick. The school rang me to come and get her and I decided, without prior notice, to pick up ds at the same time. I walked into a class of about 15 littlies - there was complete calm, some were 'reading' on a playmat, some were colouring, some were making paper collages. They all seemed happy and very content but there was no sign of the raucous chaos that I was used to in an English Nursery - no one was running around, or shouting, or crying. When I remarked to the teacher how calm and quiet it all was, she took me through to another room where another six or so children were asleep on little beds for the siesta. "This is the quiet time for the younger ones" she said. When I asked how she kept all those children quiet and happy and got half a dozen to sleep simultaneously, she looked at me as though I was mad and just said "Mais c'et normale, Madame".
This is a school, btw where my children were blissfully happy - and no corporal punishment was used at all.
On the other hand, I find the french to be generally very loving, interested and tactile parents and children are loved and cherished in society and are an integral part of daily life. In one pyrenean village, the village cafe serves the children from the local school first, before opening to the locals and the menus are posted weekly at all schools outside the school gates so that parents do not duplicate the (three course!) meals served to their children.
French nursery staff, teachers and hospital staff will kiss and hug the children. The large local hospital has benevolent "dormeuse" (dodgy spelling!) who are police checked but who come in every evening and help put the little ones to bed, play with the older children, read stories or settle fractious babies.......