Hundreds of French words are commonly used in English, and about a third of all English words may be of French origin.
The full answer to this question depends on what you mean by “French words”.
In terms of current French words widely used in English, there are hundreds – think of au pair, en suite, risqué, faux pas.
The more complex question is how many English words are of French origin.
A 1973 study of 80,000 English words suggested 28.3% were of French origin – a fraction less than the 28.34% that were of Latin origin.
A further quarter came from Old and Middle English, Old Norse and Dutch.
Other sources suggest the French influence could be even greater – with up to 45% of English words coming from French.
This question was asked on Twitter by @strudelmonkey, who also wanted to know about the origin of the word centre (one of many words in common use in both English and French).
It seems the word comes to us from the Latin centrum, via Old French in the 14th Century.