The slow change to English from Norman French took place over the two centuries following the conquest. It's impossible to pinpoint an exact "moment" when one language was preferred over the other, but one of the key elements in the loss of French as the operating language was the loss of most of the French territory under King John, and the later ascension of Henry III.

So, the first thing is that for medieval authorities, language was essential to defining a gens, which translates to "people" or "nation." Bartlett presents a strong argument that the idea of a gens is similar to an ethnicity or race. Thus, Bede's work Historia ecclesiastica gentis Anglorum is usually translated at "History of the English People" but it might be just as easily translated as "English Nation" (R. Bartlett, "Medieval and Modern Concepts of Race and Ethnicity", Journal of Medieval and Early Modern Studies Vol. 31 (2001) pp. 39-56). Similarly 400 years later, William of Malmesbury frequently uses gens to describe Franks and Anglo-Saxons (ibid, p. 43). The use of gens was not always necessary to indicate a nation as Henry of Huntingdon titled Historia Anglorum (History of the English People) shows. However, even Huntingdon uses gens when describing people like the Huns (Oxford Medieval Texts edition, 1996 - p. 65).

So, all that to argue that a people's language and their identification as a people/ethnicity were closely linked (this point is also developed by Carpenter in Struggle for Mastery which I rely heavily on). So, in the years following the conquest, a substantial portion of the new Norman lords held little land in Normandy, and instead spent their time in England (Carpenter puts the number of new Norman landholders at 8,000). This new group of gentry attempted to maintain a level of distinction over the former English landholders, marrying within their own gens and speaking French. Despite their efforts, many of the new gentry did marry women of English descent, and through conversation with their wives and landholding Englishmen, the gentry began to learn some English. This general assimilation of the Normans to English language occurred over the course of the twelfth century, but had made sufficient progress that by 1178 the author of The Dialogue of the Exchequer could claim that

“the English and Normans live together and marry...the nations are so mixed that it can scarcely be decided…who is of English birth and who Norman (Quoted in Carpenter, Struggle for Mastery p. 5).

To be sure, there were still many noblemen who retained a Norman identity. Richard I certainly did not consider himself an Englishman, and spoke no English – only French and Latin. At the close of the twelfth century, the King likely did not speak English, but John’s Barons probably did. Around the time of Magna Charta, the declining number of Norman knights made it so that impaneled juries had members who spoke no French (Carpenter, Magna Charta, pp. 3-4; 136-137). When John lost his holdings in Normandy (1204), some knights and barons tried to maintain their Norman credentials, in part to maintain claims to their land, and because they thought of the English as beneath them. However, there are many complaints of men that could not speak French, but none that complain he could not speak English.

After John’s death, Henry III took the throne as a boy of nine. However, as Henry grew up, he became more focused on piety and on devotion to England. Henry was devoted to the memory of Edward the Confessor, and even named his first son after the late King (Carpenter, Struggle for Mastery, pp. 353-354). Further, as Henry began appointing non-English men to his council, the Parliament grew agitated and petitioned Henry to place more native born noblemen on his council. Besides the Parliaments of the mid-thirteenth century, there were English born and speaking Barons present in Henry III’s court (Carpenter, Reign of Henry III, pp. 190-191). These native-born elites further cemented the use of English among nobles. By the time of Henry’s death in 1272, most of the nobility spoke English. It was less of a refined language than Latin or French, but it became a lingua franca when addressing wives, workers, and other free English men.