Do a search on Google or other good search engine, few places should come up.
There's Blanc Plume out in Kansas which offers mail order service.
As tastes and other things changed demand for true "French hand laundry" services declined across country. There are only a few places left in entire USA that still do things the old fashioned way.
Everyone else is pretty much "hand finished". Meaning basically things are washed with everyone else's, dried, put through an ironer or press, then finally touched up "by hand".
There are still a few Chinese hand laundries in New York City. But their model is what it has been from day one. Things go out to a wholesale laundry and either are ironed there, and touched up when brought back to shop. Or, sent back dried and store uses a steam iron or maybe press to finish.
https://books.google.com/books?id=u...6&focus=viewport&dq=mrs+roles+private+laundry
If you want the job done well, hand laundry (French or whoever) is rarely cheap. It takes skill, effort and time not just in how things are washed, but the ironing as well. Then there is the simple fact of laundry economics 101: you can do lots of it at lower prices, or smaller amounts and charge more. It has to be one or the other mostly for places to stay in business.
When you see offers for sheets or other linens "hand ironed" for very little money that's a tip off they use wholesalers or other methods to batch process much of the work, with only some hand finishing.
New York Times did an excellent article on struggles of one Chinese hand laundry a few years ago.
https://www.nytimes.com/2016/01/17/nyregion/laundry-service-in-new-york-city-brooklyn-san-toy.html