"Promenade" has been part of English since the 1560s, when it meant a leisurely walk taken for pleasure or to be seen by others. English simply borrowed the word whole from French, where "promenade" meant "a walking" or "a public walk." The French word itself came from the verb "se promener," meaning "to go for a walk"—so the spelling has stayed close to its French roots the whole time, which is why it still looks and sounds a bit foreign to English eyes, with that final silent-ish "e" and the French rhythm to it.
But the trail goes back further than French. "Se promener" descended from Late Latin "prominare," meaning "to drive animals onward"—picture someone herding cattle or sheep forward. That word broke down into "pro" (forth) and "minare" (to drive animals by shouting at them), which in turn came from "minari," meaning "to threaten." So a word that once conjured images of a farmer yelling at livestock to keep moving gradually softened over centuries into the idea of strolling calmly for enjoyment. By the 1640s, English speakers were also using "promenade" to mean the place where you walk, and by the late 1700s it specifically meant a walkway along the sea. In Victorian Britain, the word picked up a racier connotation too, referring to certain music halls associated with scandalous nightlife, and by 1887 it had gained the more innocent, familiar meaning still used today: a school dance, or "prom." The verb form, "to promenade," meaning to stroll about for show or exercise, followed shortly after in the 1580s, borrowed directly from the noun.
promenade (n.) 1560s, "a leisurely walk, a walk for pleasure or display," from French promenade "a walking, a public walk" (16c.), from se promener "go for a walk," from Late Latin prominare "to drive (animals) onward," from pro "forth" (see pro- ) + minare "to drive (animals) with shouts," from minari "to threaten" (see menace (n.)). Meaning "place for walking" is from 1640s; specifically "walkway by the sea" (from late 18c.); British sense of "music hall favored by 'loose women and the simpletons who run after them' " [The Observer, Jan. 18, 1863, in reference to the Alhambra in Leicester Square] is attested from 1863. Sense of "a dance given by or at a school" is from 1887. also from 1560s promenade (v.) "to make a promenade; walk about for amusement, display, or exercise," 1580s, from promenade (n.). Related: Promenaded ; promenading . also from 1580s