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 Starfleet starship Enterprise, had a painting of 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 HMS Enterprize, specifically, sailed almost 400 years ago. (ENT: "United")
Background
Archer's painting was drawn by Star Trek illustrator and designer John Eaves. It is an almost exact copy of a photo of the US Navy frigate USS Constitution (Old Ironsides) stationed in Boston. A picture of the first HMS Enterprize appears in the opening credits of Star Trek: Enterprise.