Why did the negotiations between Henry V of England and France fail?

Short answer

The two accounts cited in your question are not so much contradictory as very short versions of what was a lengthy series of negotiations over many months. The 1360 Treaty of Bretigny, which ceded sovereignty over large parts of France to Edward III, was an important part of Henry V’s demands but the English King wanted more than just French acceptance of the treaty.

For the French, even just accepting the treaty was never something they were prepared to put on the negotiating table, a key point being their refusal to cede sovereignty over the territories mentioned therein. In short, the difference between what the English wanted and what the French were prepared to offer was considerable.

These negotiations took place against a background of the rivalry for influence over the French king Charles VI between the Armagnacs and the Burgundians (under John the Fearless), as well as on-off negotiations between the English and the Burgundians.

Details

Henry V came to throne the son of a usurper. Although his father, Henry IV, had successfully fought of rivals to the throne, the new king still faced plots and saw the need to legitimize his position in the eyes of his countrymen. An effective way to do that was to reignite longstanding claims to the French throne, something which his father had been largely unable to pursue due to the extent of internal threats. Through these claims, and by skillful use of propaganda, Henry V was effectively able to unite the country behind him. His demands showed that he had no intention of making the same mistakes Richard II had when signing the Treaty of Paris in 1396. The treaty had

…resolved nothing. It simply preserved the status quo by imposing a truce on the belligerents and their allies for a period of twenty-eight years from the expiry of the current truce in 1398 until September 1426. The status quo was extremely unfavourable to England.

Source: Jonathan Sumption, ‘Cursed Kings: The Hundred Years War (vol 4)’

Henry’s approach was more strident, in part because the political conditions of the time were favourable:

When his ambassadors met those of the king of France at Leulinghen, near Boulogne, in September 1413, they began a lengthy lecture on Edward III’s claim to the throne of France and the unfulfilled terms of the Treaty of Brétigny. They even produced a selection of “most beautiful and notable books” to back up their demands with documentary evidence. … The French responded by quoting Salic Law and denying that the kings of England were even legitimate dukes of Aquitaine, let alone kings of France. In the stalemate that followed, all that could be agreed was a temporary truce to last for eight months.

Source: Juliet Barker, ‘Agincourt: Henry V and the Battle that made England’

Nonetheless, before the end of 1413 ambassadors from France arrived in London. They had been

… empowered to discuss a lasting peace and, “for the avoidance of bloodshed,” Henry declared himself ready to hear what they had to offer. He even agreed that the best prospect for securing peace was that he should marry Charles VI’s eleven-year-old daughter, Catherine, and undertook not to marry anyone else for the next three months while negotiations continued. Four days after the truces were signed, Henry appointed a low-key embassy to France, headed by Henry, Lord Scrope, which had powers to negotiate a peace, arrange the marriage and, if necessary, extend the period during which Henry had promised to remain single.

Source: Barker

Despite these initial, outwardly positive, signs

At some point in the spring of 1414, Henry had called a meeting at Westminster of the great council of the realm… to discuss and approve a resolution to go to war. Far from slavishly backing the idea, the lords of the great council delivered something of a reproof to their king, urging …. him to negotiate further, to moderate his claims and to ensure that if he had to go to war it should only be because all other reasonable avenues had been exhausted and he had been denied “right and reason.”

Source: Barker

Thus, Henry sent a further set of ambassadors to France in August 1414. After initially laying claim to the throne of France, they compromised and demanded sovereignty over practically every territory that had been held by English kings since the time of William the Conqueror:

Henry would accept Normandy, Touraine, Anjou, Maine, Brittany, Flanders and a fully restored duchy of Aquitaine in full sovereignty, together with the lordship of Provence, the one million six hundred thousand crowns outstanding from the ransom of Jean II of France and two million crowns as dowry for the Princess Catherine.

Source: Barker

Map showing the territories where sovereignty was ceded to Edward III under the Treaty of Bretigny. In addition, Henry V also demanded sovereignty over all regions along the north coast of France. The French were only prepared to allow Henry the Bretigny territories as fiefdoms. Map source: The Map Archive

The French response, unsurprisingly, offered considerably less:

These preposterous demands, amounting to about half the national territory of France including its entire Atlantic seaboard, were answered by the Duke of Berry with surprising equanimity. He told the ambassadors that no definitive answer could be given in the absence of both the King and the Dauphin. But he would give them a provisional answer. He brushed aside the English claim to the French crown as unworthy of serious consideration. He ignored the claims to the old Angevin provinces and pointed out that Provence was not even part of France. But he was more accommodating when it came to the south-west. The French, he said, were in principle prepared to consider restoring all of the provinces ceded to England at Brétigny except for Poitou (part of Berry’s own appanage) and Limousin. But any territory which they restored would have to remain part of the French kingdom and be held as a fief of the French King. As to Henry’s financial demands the Duke said that the French government would discuss the arrears of the ransom when the territorial concessions had been agreed. They would pay a reasonable dowry upon Catherine’s marriage but it would not be 2,000,000 écus; 600,000 was the sort of figure that they were used to paying. This seemed promising enough. According to the chronicler of Saint-Denis the English ambassadors seemed satisfied with the Duke of Berry’s answer. But they had obviously hoped for better. How much better is hard to say but the breaking point is likely to have been the French insistence on retaining ultimate sovereignty over Aquitaine.

Source: Sumption

Back in London,

Early in October 1414 the King returned to Westminster to preside at a great council. The assembly had been summoned to consider the ambassadors’ reports…. They thought that the results of the last embassy were promising enough to be followed up. Henry, they advised, should do nothing that might shed Christian blood or displease God until it was clear that diplomacy had failed. Another embassy should be sent to France to explore any ‘reasonable mene way’ to achieve a satisfactory compromise. Meanwhile the King should prepare an invasion of France in case the attempt failed….. over the following months it became increasingly obvious that Henry was only going through the motions of diplomacy, part of the careful preparation of public opinion for war. No one expected the French government to concede the critical question of sovereignty over Aquitaine.

Source: Barker

Up to this point, while the English had been negotiating with the French, the French had been fighting amongst themselves with the Armagnac and Burgundian factions vying for supremacy at the court of Charles VI, who was frequently incapable of governing due to bouts of madness. This, obviously, played into English hands. However, even when the rival French factions suddenly came to terms, the English position softened a little. The concessions included 1.5 million ecus for the dowry and dropping the demand for Normandy, but on most of the rest they would not budge. That included full sovereignty over the territories mentioned in the Treaty of Bretigny. The French would not agree either to the dowry, offering 800,000 instead, nor on the issue of sovereignty. Thus,

On that note the negotiations came to an end. The two sides exchanged memoranda recording their positions.

Source: Sumption

Barker concludes that

Henry V had not expected any other outcome. Four days before the French made their final offer, he had summoned the mayor and aldermen of London into his presence at the Tower and informed them that he intended to cross the sea to recover his rights by conquest.