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Attila went after the jackpot of Italy the next year and the Arabs held on to southern French cities for quite some time.”
So it can be said that Attila never dare to come back and went for softer targets.

Then what towns do you have in mind exactly? In 721, the Arabs failed to take Toulouse. Narbonne was retaken in 759. So, what is the quite of time?
In 752 they were pushed back to the south of the Aube River (20 years after Poitiers) and in 778, Charlemagne started an expedition in Spain and even took Gerona. They will still conduct some razzia, but Poitiers (732) was the highest point they Arabs did reach. And it is quite deep in the Frank Kingdom.

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