Fall River is a city in Bristol County, Massachusetts, United States. Fall River's population was 94,000 at the 2020 United States census, ma…Fall River is a city in Bristol County, Massachusetts, United States. Fall River's population was 94,000 at the 2020 United States census, making it the tenth-largest city in the state. It abuts the Rhode Island state line with Tiverton, RI to its south.