as noted above, cake delivey is not something commonly available from local bakeries. Normally, every neighborhood has one bakery open on Sunday morning; and you might want to just bring home a selection of fancy pastries instead of one cake if they don't have the type of cake you have in mind available. It would be fun to let the kids help you select.
But if you do want a fancy cake on a Sunday, though, you can take the métro to one of the grand dept stores (now open on Sundays) where their upscale food halls do have ready made beautiful fancy cakes available every day including Sundays. (I particularly love the bakery section of La Grande Épicerie at Le Bon Marché. You can also buy many very fancy already prepared dishes there if you want to eat at the apt.
(we often bring dinner home from there if we have not had time to cook; so convenient now to have it open on Sundays!)
If you want a really nice restaurant for dinner which is open on Sunday and will be informal enough for the kids as well, I would recommend La Rôtisserie de l'Argent, which is an annex of La Tour d'Argent: https:/…
(easy to get to from where you will be) Perhaps the kids can share a main course, if you want to keep the cost down; the portions at this restaurant are unusally large for Paris (many people do take home "doggie bags" from here, which is not as common elsewhere in Paris)
Edited: 23 October 2017, 00:30