The thin cut, originally double-fried in fat (not oil), is a Belgian innovation, derived from a French technique, devised by the cooks at Versailles, to fry potatoes in the very late 18th century (an one of the first recipes for potatoes that the higher classes accepted to eat). The French originally fried much fatter, even and rectangular cuts (that recipe still exists, once disposed into proper little squares constructions it becomes pommes Pont-Neuf. That's what Jefferson is believed by historians to have served at a White House dinner - that's what he would have been served in Europe.), the Belgian refined the technique, and made it a snack/dish (the French rather served them in very small quantities as a side, originally in fine cuisine, later in Bistro cuisine, and as a snack this time inspired back by the Belgians).

Historians of material economy have destroyed the legend of deep-fried potatoes originating from fishermen communities in Belgium in the 17th century. It's possible that a dish of potatoes roasted in fat in a pan existed to go along pan-fried fish, but deep-frying by the poor at the time was materially impossible.. they could never afford the fat.

"French Fries" as served today in the US/Canada are rather mostly derivatives of the English "chips" recipe (itself inspired by the French/Belgian techniques). I have a recipe for them in a French-Canadian cookbook from the early 19th century. It calls the dish "English-style chips", and suggests to make them in oil rather than fat, so they would be suitable to accompany fried fish on Fridays. "Fish and chips" have spread through the whole Commonwealth. It was especially popular in Montréal, because of the Catholic majority. It lost it's popularity only in the early 20th century, when the river became too polluted to provide fresh fish. Fries lost popularity too, until on the one end the American-style "dinners" spread them again, with hamburgers etc. and on the other end the east-european Jewish community, as they did around the same time in NYC, spread the popularity of Delicatessen in Montréal (the competition is still raging between us and NYC has to who serves the best Deli).