In the First Aquitainian War, England and France had fought for the land of Aquitaine, without coming to a result. England still wished for enlarging its part of France, and France wanted to own all of it.
While it went promising at the beginning, in 1421 France broke the coalition by making a separate peace with the Netherlands, giving emperor Gerhard II Flanders, which was incorporated into the Netherlands. Now, the tides turned again: Storming the conquered cities with cannons and relying on their greater manpower, the French slowly drove the allied English and Castillians back.
In 1424, the Cortes, the Castillian estates, protested the high costs and low results of the war. King Pedro III was sorry about it, but had to leave the war too. He had better things to do, in fact: Interfering in the Portuguese Civil War.
The war ended unexpectedly in 1426 when the pope and the Anjou king Roberto III of Naples asked the French king for a crusade against the Rum-Seljuks, king Charles IV agreed to fight the Great Napolitan War instead. He made peace with the English, leaving Guyenne in their hands; king Richard III had to accept it as a fief, though.
Neither England nor France was really happy with this result of the war, so it was no wonder that the Third Aquitainian War would follow later.