Your film is
Diva (1981). I haven't seen it, but found it in IMDb with some clues from your description.
If you like chases, you'll love the chase in "The Matrix Reloaded". Not an old film, sorry, but the chase is superb. Two people on a motorcycle, going against the traffic on a highway, chased by a car. Completely impossible, but it takes place in the Matrix, so anything goes.
An old film I can recommend is "Les uns et les autres", a tale of generations of musicians and dancers from different countries, from before WWII until 'now' (1981).
This message has been edited by Parasomnium, 19-Jan-2006 03:16 PM