I do not have eczema but I am VERY sensitive almost all things that touch my skin. Generally things that at made for babies are made with extreme sensitivity in mind. I use this and I am completely fine. I still might try a small area on your child first to make sure there is no reaction!
It is advertised as safe for sensitive skin. I'm an adult with eczema and almost always buy sunscreen for babies, this specific product included. Just make sure to test a small area and always read the ingredients closely!