This can help...?
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.
In the U.K., fried fish had been on sale by street vendors since the 1600s. In 1864, a brilliant (but, alas, unknown) Brit teamed French fried potatoes (called "chips" in English) with fried fish, to create the famous and popular fish and chips.