While the previous writeup lists phrases that still are clearly French, I'll speak about English words that derive from French words. According to Howard Woods in Syllable Stress & Unstress (1978), this is the case of 28.3% of all English words, although these words only account for 15.2% of word usage in a daily newspaper.

The influence of the French language on the English language began when William the Conqueror seized England in 1066. At the beginning, the Normans only used French to govern England but, after France seized Normandy, the use of French gradually declined. Major social changes caused by the Black Death, in the 1340s, increased the influence of the lower or middle classes, who spoke English. In 1362, the parliament adopted English as its official language and everybody spoke English by the end of the century.

In the meantime, no less than 10000 French words had entered the English language, especially in domains controlled by the Normans:

The introduction of French words was later blamed on Chaucer (second half of the 14th century), but maybe the Romance words he used had already been introduced in oral language or in lost writings. Besides, maybe the old Germanic words were already dying before the new words were adopted.

During the 17th and 18th centuries, linguistic nationalism rose in England and the influence of French was considered by some people as a tragedy for the purity of the language. The mathematician and grammarian John Wallis claimed that any influence of Latin ought to be removed from the vocabulary as well as from the grammar. As an aside, he explained his theories in the first systematic English grammar, which he wrote... in Latin (Grammatica Linguae Anglicanae, 1653).

Nowadays, although English has become the de facto world language, a few French words still continue to penetrate the English language. It seems that, today as in the Middle Ages, French words are used by the elite and are seen as snob before they become mainstream words (or disappear). Gone Jackal tells me that around 1000 French words are used that way in modern English. Because I'm French, I cannot write much about this subject. I can only say that I am filled with bewilderment when I read about the opportunities for double-entendre and sexually-risqué comment in a E2 writeup.

Many sources. The most interesting and complete was http://www.uwm.edu/People/aleinss/mideng.pdf