What are the lyrics (in French) of the song featured on the soundtrack
to the film Rushmore, "Rue St. Vincent" as sung by Yves Montand, the
French crooner/actor of yore?

The complete lyrics to "Rue St. Vincent" may be found here:

Caritas
http://www.caritas.ac.jp/chansons/v/vaucaire2.html

Here is another version, very slightly different:

Le Chat Noir
http://www.lechatnoir.free.fr/historique/chatnoir/bruant/02_bruant_rose_blanche.htm

Apparently the song is better known as "Rose Blanche." Here's an
interesting bit of history involving the songwriter, Aristide Bruant:

Personal page of Earl Mayan 
http://home.earthlink.net/~klavir/utrillo_chapter_1.html

This was a challenging research project. Initially, using the search
terms "rue st vincent" and "yves montand," I could not find these
lyrics, although I found many references to the film "Rushmore." Then
I got a brainstorm. I listened to my recording of "Rue St Vincent,"
picked out a few phrases, and decided to search the French-language
version of Google, using the search terms below.

Google Web Search, French pages only:

"on n'avait pas connu" + "montmartre" + "vincent"
://www.google.com/search?lr=lang_fr&cr=&q=%22on+n%27avait+pas+connu%22+montmartre+vincent&hl=en&ie=UTF-8&oe=UTF-8&newwindow=1&safe=off

I hope this is what you were needing. If anything I've said is in need
of explanation, or if any of the links do not function, please request
clarification before rating my answer, and I'll gladly provide further
assistance.

Best regards,
pinkfreud

Exactly what I needed, and very fast.