Archer's painting of the HMS Enterprize.
Image from opening credits.
The first Human naval ship to bear the name Enterprise was a British sixth-rate captured from the French and renamed HMS Enterprize in 1705. She ultimately became the ancestor of a great line of vessels, both seagoing and spacefaring, that spanned for at least the next thousand years.
From 2151 until 2161, Jonathan Archer, the captain of the Earth Starfleet starship Enterprise, had a painting of the HMS Enterprize hanging in his ready room. (Star Trek: Enterprise)
While viewing the captain's display of ships named Enterprise in 2154, Shran asked Archer if he had personally served aboard the various vessels on display. Archer noted that many of these vessels were active before his time, and that the HMS Enterprize, specifically, sailed almost 400 years ago. (ENT: "United")
Background
Archer's painting was drawn by Star Trek illustrator and designer John Eaves. A picture of the first HMS Enterprize appears in the opening credits of Star Trek: Enterprise.