5 a Sec
You can find 5 a sec outposts all over Paris: Not only are their dry cleaning services reliable, but they can do a quick turn-around at great prices. They offer home (or hotel) delivery and will send a text when your pieces are ready for pickup.
Haven in Paris
This is like a luxury Airbnb. Beyond corralling really nice house stays, they offer other concierge services like drivers, babysitters, tours, and more. Their blog—www.hipparis.com—is full of great city-wide recommendations.
17 Avenue George V
Baby Prestige carefully vets their bilingual babysitters, and is able to accommodate on fairly short notice. They also offer more long-term childcare options for residents.
At Your Service
The American staff here know Paris intimately: Not only will they send you to the best spots, but they'll get you the best tables and hotel rooms, too. They also provide property management services to residents.