The major influence of French words in the time right after the Norman conquest was that French became the prestige language of England. When one language becomes a prestige language, many of its words (especially in areas of culture and power) enter into the native language of the country.
This is how French impacted the English language. French words entered the English language in areas of power (government, military) and in areas of culture (food, entertainment). These words like baron, dame, lieutenant, enemy, pork and beef came to be used by people who wanted to get themselves into power or who wanted to act like they were high class. Eventually, they filtered down to the rest of the people.