c. 1600, "a way of approach" (originally a military word), from Middle French avenue "way of access" (16c.), from Old French avenue "act of approaching, arrival," noun use of fem. of avenu, past participle of avenir "to come to, arrive," from Latin advenire "to come to, reach, arrive at," from ad "to" (see ad-) + venire "to come," from a suffixed form of PIE root *gwa- "to go, come."
The meaning was extended to "a way of approach to a country-house," usually a straight path bordered by trees, hence, "a broad, tree-lined roadway" (1650s), then to "wide, main street" (by 1846, especially in U.S.). By late 19c. in U.S. cities it was used to form the names of streets without reference to character.