Note this is not necessarily a 'no Islam' scenario, more one where for whatever reason the Byzantines and Persians manage to contain the initial Arab explosion and they don't get much further than Egypt/Palestine/Mesopotamia. The reason I point this out is to avoid a 'uber-Justinian-type Byzantine Empire just reconquers them' idea: assume Constantinople more than has its hands full dealing with the Arabs.
So, without the Arab invasions or a Byzantine reconquista, how would the culture and structure of Visigothic Spain develop? Would it become perceptibly Germanised, or more like France, with the culture of the Latin majority generally winning out over that of the Germanic overlords?
Or would Spain just be conquered by the growing Frankish empire instead, as the Visigothic kingdom was already declining anyway?