John II was captured after the Battle of Poitiers in 1356 and taken to Britain. Why did they wait and ransom him only to fight the French again? The ransom was 4 million pounds, but that could be recovered, through pillage of Paris.
One reason could be, there was a feudal system, and each feudal lord kept his own forces. But then, they could have at least seized the central territories, around Paris, with little resistance; and rest of France with a lesser resistance as the feudal lords did not have a central figure to rally around. The English already held Aquitane and Gascony, and could further logistically support campaigns.
Capitalising on the discontent in France after the peasant revolt, Edward assembled his army at Calais in the late summer of 1359. His first objective was to take the city of Rheims. However, the citizens of Reims built and reinforced the city's defences before Edward and his army arrived. Edward besieged Rheims for five weeks but the new fortifications held out. He lifted the siege and moved his army on to Paris in the Spring of 1360. The suburbs of Paris were sacked but the city held out.
In 1362 John's son, Louis of Anjou, a hostage in English-held Calais, escaped his parole and refused to return. When John found out, ashamed at the actions of his son he felt duty-bound to return to captivity. He left Paris and gave himself up to the Captain of Calais, who returned him to his honourable captivity in England. He spent the rest of his reign there and died in London on 8 April 1364. John's funeral, in England, was a great chivalrous affair and he was honoured as a great man by the Plantagenets.
The parallel hostility and upholding deals is counter-intuitive. If Edward III intended to continue his conquests, would it not have made sense to not have signed the Second Treaty of London letting John II go in 1359.?