The River is based on a novel by Rumer Godden, the same author who wrote Black Narcissus, which was adapted by Powell and Pressburger a few years before. I mention this up front because I think most people who know both Renoir's work and Powell's and Pressburger's work would think the British duo had made this film as well. Along with the technicolor cinematography and British central character, the film has the global reach and dignified air of their previous films. Interestingly, Godden was apparently dissatisfied with their adaptation of Black Narcissus but enjoyed this movie. I found Black Narcissus to be a visually appealing and fascinating psychological exploration of the edges of Western civilization, while I found The River extremely forgettable.
The biggest problem I had with the film was the narration, which seemed both unnecessary and overused. It certainly doesn't help that the lead character of Harriet is arguably the least interesting character in the film. Especially today, with The Help nominated for a ridiculous amount of awards and the still-evident impossibility of a mainstream film with a non-white character at the center of a movie about non-white people, it is difficult for me to get past the core gravity of the story's narrative.
One major reason I came away so disappointed in The River was that I had high hopes for the film's ability to convey a sense of place in a location that is underrepresented in Western film (and in the Criterion Collection - only a handful of films are set in India, only two films out of over 600 were bankrolled there). While I wouldn't expect a French filmmaker like Jean Renoir to be able to deliver authentic, specific insight into Indian culture, I had hoped that his eye would be trained on Indian culture, rather than the colonial culture that had been overthrown in the previous decade. This is not the fault of the film - which has no responsibility other than to be the best version of itself it can be - but it contributed to my apathy anyway. The film's documentary qualities (depicting the river, various ceremonies, the life of the locals) helped redeem it somewhat, but overall it wasn't enough to draw me in completely.