We took our kids when they were 10 and 12.
It was in March, so a bit warmer but two things stood out for the 10 year old. And they were simple. Near the Louvre in the park is a small trampoline park. He loved it and made french friends. It is near the Westin, so on the western edge of the park. Nearby is a great place for treats & hot chocolate, Angelina's.
In Luxembourg Gardens there are some interesting things for kids including a Marionnettes, carousel, and swings. Of course, this assumes it is warm enough to be outside.