The Lafayette Durfee Foundation is looking for any information on the early layout of Fall River, then known as Lower Freetown.
The Foundation has a map dating to 1812, but we'll be seeing if we can find anything earlier.
The City of Fall River notes on it's website that limited historical land use maps may be available.
The Library of Congress may be essential to your search.
The Massachusetts Historical Society has the largest collection of historic Massachusetts maps. Starting there would be a good idea. They have digital collections, but you may want to contact them.
The Fall River Historical Society also has a collection of maps in their Ephemera collection.