Well, for a start, they'd probably stop at the Pyrenees. There's a good reasons the Visigoths never really expanded into Franciua or vice-versa; they make the perfect boundary between two nations.
The Cathars would probably escape to Muslim Iberia, but I doubt there's enough of them to make a big cultural impact, and I suspect they'd simply convert to Islam anyway; even if they aren't actively forced to convert, there'll still be substantial pressure to do so.
The barrier of the Pyrenees means that once the Muslims have conquered Spain and held it for a generation or two, it'll remain theirs. We'll probably see the New World discovered by Spanish Muslims, and today Arabic would be the world's most spoken language.
What kind of effect would a unified, Muslim Spain have on Francia? Would we see it centrallise much more than OTL? Would there be Muslim raids into the southern reaches of Francia?
Linguistics would be interesting; I'm imagining a fusion of Gothic, Latin and Arabic. It'd be one very interesting language