An historian stated in, a source i can no longer put my hands on, that franks adopted it massively after the duke of Aquitaine destroyed a muslim army at Tolosa.

In my opinion, it looks a bit like a "magic explanation". I'd say that constant fighting between franks and muslims around the Pyrénées (and the friendly relations between Odo, duke of Aquitaine and the muslim leader in Narbonne) just allowed a slow adoption of the stirup.

Before the stirup, franks did not rely heavily upon cavalry. After the stirup, the change is radical (insert paladins here).