Hi Taz,
The direct area of the Hotel consists of mostly Japanese restaurants…There are 2 great places I would rec. one Japanese ‘gourmet’ & one with Soufflés as specialty—basically everything on the menu is a soufflé

Delicious!…I’m bad with remembering names but if you are interested I can ask my friend…
-There is a boulangerie & monoprix supermarket right near the hotel if you want to picnic.
-Close by is place Vendome with the Ritz & hotel Costes…or you could stop to have drinks at fancy hotel Meurice

Also the dept stores are at walking distance.
-A really nice longer walk with baby is to cross the Tuileries and then along & across the Seine towards Saint Germain where you will also have a larger choice in Restaurants…
I love to stay in this area- it’s a little ‘bourgeois’ of course but so nice & comfortable with a baby.