And French in turn was influenced a lot from Latin. Which means a lot of the French loan words have their origin in Latin. And of course Latin is actively used to this day in the Catholic church and the Church of England. Latin was widely used for written communication for quite some time. Most people couldn't read or write. But that impacted a lot of religious, scientific, legal, etc. communication and words. English also has a lot of loan words from other languages. Lots of nautical terms have an obvious Dutch origin, for example.

It's not just influence: French descended from Vulgar Latin, with a lot of influence first from the Gaulish (Celtic) substrate and then from the Frankish (Germanic) conquerors.