It really depends what you mean. If by "Visigothic Spain" a Kingdom ruled by monarchs who can trace their heritage back to the Visigoths, than this is OTL. However, if you want one continuous state with continuity of institutions, etc., then I think all you need is for the Visigoths to put up a little better defense against the Muslisms so that you get a rump Visigothic Spain in place of Asturias. I'm not sure what institutional change was necessary for weak Asturias to transform itself into Leon and Castille capable of beating back the Muslims, but i'm assuming the same could take place in the Visigothic state.
So, I guess what I'm saying is that not much change would be necessary, really. Basically, just mimick OTL, but with a slightly more organized Asturias.