check out the famous cemetery with Zola and his girl friend, etc. Catacombs are not too far by foot I believe nor the Eiffel Tower no Egouts (tour of the sewers) - Ecole Militaire also close enough.

I don't know about any music unique to a Sunday or exactly what you are looking for in that regard. There is a Sunday "arts" market on bd Edgar Quinet leading east from the train station, so you can check that out. I've never seen anything I liked much in it, and the stuff is expensive, but you might like it. It's not the typical roving anything-goes type of market but artists selling their own work (paintings, jewelry, etc.). Here's info you can decide. It's worth a look http://www.marchecreation.com/index-en.html

I am not positive it is there "late afternoon", though, most markets close up in early afternoon.

I'm not clear on whether you are arriving in Paris or leaving it, but late Sunday afternoon is not exactly a happening time for anything, to be honest. There are a few interesting small museums in the area I can recommend -- the one right near the gare about WWII and the Resisistance is good http://www.musee-resistance.com/, and so is the photography place Fondation Cartier depending on what is on exhibit http://www.henricartierbresson.org/infos/INFO_acces_fr.htm

There are a few other minor museums that are okay, depends on your interests (like the Poste museum which I quite liked or Bourdelle). And the cemetery if you like loking at some famous graves (or not). Sartre is in there along with beauvoir and a few famous artists or musiciens.

I don't really understand if you have a car with you or what, there is the rue Daguerre pedestrian street market and the catacombs as mentioned but they are a bit of a hike away or, of course, a metro stop or two. Of course, the catacombs close at 4 pm for entry, so that doesn't really sound feasible.

You can check out www.whatsonwhen.com to find out what events might be happening that day.

The Edgar Quinet market closes at 3 pm on Sundays.

Many thanks folks.There are some interesting suggestions here.

Here's a link to a thread I started last fall when I was planning to explore Montparnasse. There were lots of helpful responses.

http://www.fodors.com/community/europe/exploring-montparnasse-suggestions-please.cfm#last-comment

Thanks MaineGG.It`s certainly all there!

Rue de la Gaîté is the main entertainment street of the neighborhood.