Toups & Co Baby Wash + Shampoo
$20
Gentle 2-in-1 baby body wash and shampoo with a very short list: water, saponified coconut oil, aloe, guar gum. Mild enough for newborns and the whole family.
It doubles as a shampoo, so treat it as a gentle all-in-one rather than a dedicated hair product.
A US source in the The Unmasked Face directory. Check that it ships to Europe; where it does not, the directory lists a European alternative alongside it.