Only a few of the previous comments on this movie has mentioned the use of music. Just like in Trois Couleurs Bleu, the music of La Double vie de Véronique is very indivisible from the film: the visual and the auditive form a united whole and also elements of it are directly part of the story. And when it comes to music made for film, Zbigniew Preisner's powerful score for this one is as good as it gets.
When there is little dialogue, it is not just the images and expressions on Irène Jacob's face that tells the story, but also the powerful strains of music intermingled with it.
Even with just these elements in place, it would be a movie worth seeing, though obviously a narrative based in little extent on dialogue and with less emphasis on a clear-cut story than your average American movie is unfortunately lost on some of the earlier commentators.
And even this seemingly sparingly laid out narrative reveals itself to the careful watcher to be a rich tapestry of symbols, metaphors and hidden meanings. Kiéslowski, just as in his other movies, demands participation of the viewer, and the one who expects passive entertainment has found the wrong film to watch.
Krzysztof never liked discussing meaning when it came to his movies, but liked keeping that up to the viewers, and few other directors have ever been able to lay out more food for thought and fruitful interpretation than him.
I saw the Three Colours trilogy before seeing Véronique, and the many similarities, both musical and in visual narrative, makes it feel like it almost belongs together with those three to form a quartet. In some ways it has more in common with Blue than Red and White do.
Had Juliette Binoche also been cast in the role of Véronique, as I understand that Krzysztof originally had intended, the similarities had been even greater. She was, however, occupied with shooting Les Amants du Pont-Neuf at the time I believe, and so Krzysztof opted for the less experienced Irène. I don't think the film is any worse for it: she is brilliant, and not just a pretty face as some people put it, but a very intelligent and aware actress as anyone who has seen her interview for the Red DVD release should discover if they haven't already.
In short: a wonderful film, wonderful music, great acting. But not a movie for everyone.