mwestwood's answer is very good, but it contains what's probably a typing error: "Middle English" (not "Old English") is the language of Chaucer (actually, it's late Middle English.)
The enormous influence of French on English through the Norman invasion, enormous enough to cause linguists to identify c. 1100 AD as the beginning of the Middle English period, illustrates an important point about how we talk about language change. There are two main models for talking about language change.
The Stammbaumtheorie (family tree theory): Languages may be said to have "parent" languages (e.g. the parent language of Middle English might be Old English or Germanic or even Proto-Indo-European). Instead, they often experience powerful influences through time. If anywhere in the family tree, French might be seen as an evil stepmother. Also using this model, we might say that "beef" and "cow," because both words are direct descendants of the Proto-Indo-European word *gwou-, are distant cousins. This model allows for the construction of a language chart that is clear but also simplistic.
The Wellentheorie (wave theory): Waves of language change may be said to roll across the linguistic landscape, strongest at their point of origin and growing weaker as they travel long distances. In this model, French becomes a hugely powerful seismic shock originating not from abroad (as seen in the pre-1066 loanwords from French into English) but from the very political center of England. This model allows for the construction of a multi-layered language map that is extremely messy but also probably largely accurate.
Both models are good. Each model makes up for what the other lacks.
After the Norman Conquest of 1066, French became the language of the nobility, almost all of whom were the Norman conquerors since they virtually slaughtered the Saxon lords in the Battle of Hastings. Everything that was written was in French, not just government works. Literature such as the legends of King Arthur, for instance, were written in French. Much of French became mixed with the language of the Saxons as the stewards of lands of the Norman lords had to find a way to communicate with their masters. This French/Anglo-Saxon mixture is the cause of the inconsistency of dental, dentist, dentures, with tooth/teeth, for instance. [dent =tooth in French, but tooth/teeth do not]
Some 300 years after the Norman Conquest, Geoffrey Chaucer, who himself wrote French verse, poetry in the style as well as the language of France, decided to write his Canterbury Tales in the vernacular. After this great work was published, more literature was written in Old English. Nevertheless, anyone who reads the Canterbury Tales finds evidence in the Old English of French as much of the sentence order imitates French--i.e. possessives come after the noun, adjectives also often follow nouns, words have the Old French meanings. In fact, there are many, many parallels between Old English and Old French.
Any student of French realizes quickly the tremendous impact that French played upon the development of the English language. Indeed, over 60% of the words in English are derived from French. Truly, French is the parent of Middle English and Modern English.
French came to impact English mostly through the Norman invasion of England in 1066.
After that invasion, French became the prestige language because that is what the rulers spoke. Because of this, many French words came into the vocabulary. This was especially true of words having to do with government.
However, even other kinds of words entered English usage if using them could make you look richer and more sophisticated. So, for example, this is when we got different words for an animal (cow, pig, for example) and its flesh that we eat (beef, pork). Saying you were eating "beef" made you sound more like an elite person than saying you were eating "cow."