The English language largely survived the Norman conquest, even though it was driven out of the public square for many generations. This was probably because it was already a literary language, with many readers and writers, unlike contemporary French, which essentially lacked a literature at the time. It's plausible that French literature originated in England under the influence of the suppressed English.
The famous Chanson de Roland, an epic poem of Charlemagne’s battles against the Saracens, was first written down in England in the early twelfth century. The first historical work in French was Geoffroy Gaimar’s history of the English, the Estoire des Engleis (c. 1136– 37), an accessible work in fashionable French verse based on the Anglo-Saxon Chronicle. English authors— or authors in England, often of mixed Anglo-Norman families— attained a European influence greater than ever before, and rarely equalled since.
Tombs, Robert. The English and Their History (Kindle Locations 1417-1422). Knopf Doubleday Publishing Group. Kindle Edition.
English personal names did not fare so well, though. They were largely lost:
There is perhaps nothing that distances us more instinctively from the pre-Conquest English than names: Ealdgyth, Aelfgifu, Colswein, Eadric, Waltheof (even if a few were revived during the Romantic period— Karl Marx called one of his sons Edgar). Our names since the 1100s have been overwhelmingly Norman, a personal form of cultural conquest through snobbery: William (which became the most common), John, Richard, Robert, Margaret, Mary, Emma. In a significant conciliatory gesture, the sons of Henry III were christened Edward and Edmund, signalling a link with the pre-Conquest monarchy; and the former became King Edward I in 1272.
Tombs, Robert. The English and Their History (Kindle Locations 1403-1408). Knopf Doubleday Publishing Group. Kindle Edition.
Note, btw, that "Edward" was one of those hardy name survivors of the earlier age.