That the Normans spoke French is certainly true, and although they did nor replace the language, they certainly modified it. Sometimes it is difficult to say whether English words that sound French come directly from the Normans, or whether both the words have a common route in Latin, but a pretty conclusive example it the fact that English is unusual in having different words for animals and the meat that comes from them. (Pig/pork, cattle/beef, sheep/mutton) Its pretty obvious that the animals' names come from the original English, and that these are the names given by the peasant who tended the animals. The meat was named by the French speaking nobles who consumed most of the meat. Just to emphasie the "French connection": pork, porc; beef/beouf; mutton/mouton.

However, just because they spoke French, doesn't mean that their culture was French.