I have only read your posts, so someone might have said this already
The reason the French police give is this - when they try and approach a boat in this situation, or indeed go anywhere near it to do anything, it usually result in a panic.
Sometimes there is a crush because of the volume of people trying to get away from being arrested or whatever and that makes any infants or children even more likely to be injured in a crush
Also possible is that someone will get cold water shock if knocked into the water
basically, if the boat is further than knee deep for an adult, everyone on the boat is away and over here now - because the French police won't intervene. Baby or no baby, they will not intervene.
Yes, we are paying them to do absolutely nothing.