What is the English word for "street along a river bank"?

Here in Australia we call them esplanades, although as wikipedia says, that really refers to

a long, open, level area, usually next to a river or large body of water, where people may walk.

A related word is promenade.

You can find these streets referred to as river roads, often with River Road or River Street being part of their proper names. There are many books that use the term, including The Majesty of the River Road, where the introduction begins

Along the road that follows the course of the Mississippi stand many majestic structures that have withstood the test of time.

Here a picture where it's part of the proper name, Savannah, Georgia's (USA) River Street (ref)

While embankment might describe a bank, mound, dike, levee, or the like, and is typically raised to hold back water, it may carry a roadway or railway, but not necessarily (ref):

London has the roads called Victoria Embankment and the Albert Embankment on opposite sides of the river; it also has the Strand — strand as a noun refers to a beach.

“The Embankment” generally means the path along the south side of the Thames between Westminster Bridge and Lambeth Bridge, opposite the Palace of Westminster.

As the Wikipedia article explains, Embankment does mean an earthwork built to contain a river or support a railway or road; but (as the article notes) can also refer to a roadway atop such a structure. Usually, such a use is qualified as in Victoria/Albert/Chelsea Embankment.