There seems to be some confusion regarding the name of this bridge, with some people referring to it as "Black's Bridge". As far as I know, Black's Bridge refers to the automobile bridge at the end of Mill Street, just upstream from Lock 2.
Here's the evidence:
City of Montreal and suburbs, 1875 (detail)
Electoral District of St. Anne, Montreal, 1895 (detail)
Map of the city of Montreal, 1903, Chas. E. Goad (detail)
Montreal Harbour, 1940 (detail)
Plan of the southern portion of the Harbour of Montreal, 1930 (detail)
This 1967 map detail doesn't identify the automobile bridge by name, but it does show it when it was just a road over dry land:
I don't know the proper name of the abandoned train bridge, but the Parks Canada page taP just posted refers to it as "Le pont CN-Du Port" or "The CN Port Bridge".
And check out
this page for some interesting pictures of the Lachine Canal and the Old Port from 2001.