The straightforward explanation of the term "French fried potatoes" is that it means "potatoes fried in the French manner": the verb fry can mean either sautéing or deep-fat frying, while French 'frire' unambiguously means deep frying. Thomas Jefferson, famous for serving French dishes, referred to fried potatoes in this way.
There are other, more speculative theories.
The Belgians are noted for claiming that French fries are Belgian in origin, but have presented no definitive evidence; the French have also been cited as possible creators of the dish, though in France they are often thought of as Belgian; the Belgians are the heaviest consumers of French fries. The Spanish claim that the dish was invented in Spain, the first European country in which the potato appeared via the New World colonies, and then spread to Belgium which was then under Spanish rule. Whether they were invented in Belgium or Spain, they have become Belgium's national dish, making Belgians their "symbolic" creators in Europe.