Une rivière, un fleuve
Another insight mentioned that there are two French words for "river", rivière (f) and fleuve(m). http://duolingo.com/#/comment/30893
There are two ways of distinguishing them. The most common one is that a fleuve is a major river. At school children learn about the fleuves of France: Seine, Rhin, Rhône, Loire, Garonne and Meuse. Le Fleuve Bleu is the Yangtze or Chang Jiang.
The other definition of "un fleuve" is a more specialist (Geography, Hydrology) definition and means a river which discharges into the sea so it is not a tributary of another river.
The rivers mentioned above fit both definitions, My local river is "une rivière" by the first definition and "un fleuve" by the second. It is three and a half metres wide and about one metre deep.
You can use "rivière" for any of the "fleuves" unless you are taking a Geography exam, writing something formal or you just need another way of saying it is a major river.