Though not always easy to find
Dry powdered chlorine bleach is around in the USA. Lever sells small boxes meant for coin/vend laundry use but there are places that will sell the stuff to anyone.
Eau de Javel is not really big in France for laundry. Indeed it often is sold in those little sausage type containers fabric softener used to come as in the United States. However the chlorine bleach in France is usually always with the cleaning products, not laundry. For some reason French households don't mind chlorine bleach for cleaning their homes, just don't want it for laundry. Well one knows the reason, but still.
Cotton is a relative new fiber to France as much of Europe. Previous the main textile for "linens" was linen, which is very badly harmed by chlorine bleaches.
For some really powerful dry chlorine bleach commercial laundries have access to "reclaim" versions. That stuff is meant to deal with laundry so badly stained that the next stop would be the rag bag or whatever. So exposing it to strong chlorine bleach cycle falls under "nothing ventured, nothing gained"... *LOL*
Those little bleach tablets are also great to take on camping trips or if you are into "survival" type things. In the proper dosage you can use the chlorine tablets to "disinfect" water one is unsure of to make it safe for drinking.