Etymology of "French fries"

Straight Dope has a good explanation and here is the answer from the article:

For also in the 1840s, pomme frites ("fried potatoes") first appeared in Paris. Sadly, we don't know the name of the ingenious chef who first sliced the potato into long slender pieces and fried them. But they were immediately popular, and were sold on the streets of Paris by push-cart vendors.

Frites spread to America where they were called French fried potatoes. You asked how they got their name--pretty obvious, I'd say: they came from France, and they were fried potatoes, so they were called "French fried potatoes." The name was shortened to "french fries" in the 1930s.

By the way, the verb "to french" in cooking has come to mean to cut in long, slender strips, and some people insist that "french fries" come from that term. However, the French fried potato was known since the middle 1800s, while the OED cites the first use of the verb "to french" around 1895, so it appears pretty convincing that "french fried potatoes" came before the verb "frenching." The origin of the name is thus the country of origin French and not the cooking term french.

Here is a passage about how it is introduced to America from a book called "Potato: A History of the Propitious Esculent" By John Reader:

French fries get their name from French frying, a method of frying food.

The OED has French fries as originally and chiefly North American, dating to 1902 but dating to at least 1886, as found by Fred Shapiro, editor of The Yale Book of Quotations:

1886 Springfield (MA) Republican 12 Oct. 1 (GenealogyBank) REMEMBER that the place to buy Saratoga Potatoes is at No 4 Dwight-street (near State), also French fries Wednesdays and Saturdays.

An earlier name is French fried potatoes, dating back to 1856 in Eliza Warren's Cookery for Maids of All Work:

This method of French frying goes back further, as found in The Cook and Housewife's Manual from 1828: