The Normans were very much a minority, William certainly granted them positions of power as earls, bishops and landowners. A lot of the English nobles had been killed at Hastings and Stamford Bridge so there was a power vacuum which Normans were able to fill. I have some sources that may be helpful.

‘the greater part of the English earls had been killed together with their king and his brothers and other lesser nobles and soldiers’ -- Van Houts, E.M.C, The Normans in Europe (Manchester University Press, 2000), p. 106

‘English nobility was destroyed as a class and many of the native ecclesiastical leaders were deposed’ --Frank Barlow, ‘The Effects of the Norman Conquest’, in The Norman Conquest: Its Setting and Impact ed. Dorothy Whitelock, David C. Douglas, Charles H. Lemmon, Frank Barlow (Eyre & Spottiswoode, United Kingdom, 1966) pp. 123-161 (p. 130)

‘a great many Englishmen, especially those who were highest in rank and wealth, had lost their lands under William, and that the lands so lost by Englishmen had been for the most part granted out to strangers’ --E. A. Freeman, The History of the Norman Conquest of England: Its Causes and Its Results (Cambridge University Press, 2011), p. 15

‘the Normans, dividing among themselves the lands of England to be held according to English law, became Englishmen with wonderful speed’ --E. A. Freeman, The History of the Norman Conquest of England: Its Causes and Its Results (Cambridge University Press, 2011), p. 60