I have not seen a conversion between US and European sizes for girls.
I just had a customer from Europe contacting me asking what size I would recommend for ages 6 and 10.
Aargh! So I just did a bit of searching (Googling) and came up with nothing.
It seems there is a rough relationship between size and age for US sizes. The challenge is kids vary so much in their shape, at the same age.
Future project - build a conversion chart between European and US Sizes.
And of course, US Sizes for Girls, just like for Women, can and do vary a bit. For example at some stores my wife would wear a size (left blank so I don't get in trouble), and at other stores the next size up (again left blank so I don't get in trouble). Which is just frustrating.
It would be nice if a size X at Nordstrom's, was the same as a size X at JC Penney's for example. The X has no meaning as a size, and represents any number.