We stayed on the Avenue de la Motte Picquet in the 7th Arrondissement, just opposite Rue Cler, and easy walking to the Champs de Mars (great for children). Alternatively if you really want to be in the centre of things, and are going to go for self-catering, there are some absolute bargains to be had in the 1st Arrondissement, within easy reach of the Jardin des Tuileries/Louvre etc.
Sacre Couer and the top of Montmartre is pleasant enough, I just find the area surrounding it, particularly the street at the bottom with all the sex shops and beggars (can't remember the name of it) a bit meh and I certainly wouldn't want to take children near there.
We are going to Paris to meet Australian relatives who will be on honeymoon there so wanted to really stay near them to make it easier up see them. They quite like idea of montmatre & I've always loved it there too but maybe its not best idea with little ones? Where else would you suggest that would work well to be interesting, vibrant & fun for honeymooners too?
I have three young children, two with food issues so hotels are not great for us. We stayed in a self catering apartment in Paris and I loved being able to feed the children when I wanted to, put the children to bed in the next room and be able to chill out and pretending we lived there!