From Wikipedia:
Say that the Umayyad army maintained proper vigilance and thus was able to defeat Odo's army and then take Toulouse. Aquitane is now under Muslim control and the Umayyad army will be looking to continue north, to conquer the Franks. Can they do it? How far can they go?
Al-Samh ibn Malik al-Khawlani, the wali (governor) of Al-Andalus, built up a strong army from Umayyad territories to conquer Aquitaine, a large duchy in the southwest of modern-day France, formally under Frankish sovereignty, but in practice almost independent in the hands of the dukes of Aquitaine. He besieged the city of Toulouse, then Aquitaine's most important city, and Duke Odo of Aquitaine, also known as Eudes, immediately left to find help. He asked the assistance of Charles Martel, who in turn preferred to wait and see rather than help his southern rival. Odo returned three months later, just as the city was about to surrender, and attacked the Umayyad investing force on June 9.
The victory was essentially the result of a classic enveloping movement by Odo. After Odo originally fled, the Umayyads became overconfident, and instead of maintaining strong outer defenses around their siege camp, and continuously scouting, did neither. Thus, when Odo returned, he was able to launch an almost total surprise attack on the siege force, scattering it with the first attack, and slaughtering units that were resting or fled without weapons or armour.
Say that the Umayyad army maintained proper vigilance and thus was able to defeat Odo's army and then take Toulouse. Aquitane is now under Muslim control and the Umayyad army will be looking to continue north, to conquer the Franks. Can they do it? How far can they go?