Planning 2 Full Days in Paris

It's an utter pleasure to sit in this shiny new hostel, listen to covers of Jum Morrison being played in the bar, and plan my weekend in Paris.
I have been to this city before. Most recently I was here in September 2012 at the end of a cruise in the Greek Islands. Most memorably was in 1978, when I worked in Paris as a nanny. That gig pretty much set my course for life, making me a beer budget sort of person with a taste for champagne. It's certainly the reason I feel at home in France.
So, because I don't need to do the "incontournables" (the unmissables), as the Office of Tourisme's Paris est A Vous! guide I got for free in the hostel, I can go exploring based on my geographical location.
The pen in this photo points to Rue Pajol, which places me within easy biking distance of Montmartre and Batignolles, as well as the big flea market at St-Ouen.
So my rough plan is to spend Saturday north of the Seine, and Sunday south, in St-Germain-Des-Pres and Montparnasse.
Of course, as I'm traveling on Wm the Conqueror, I'll find a way to ride past the biggies, like the Eiffel Tower and Notre Dame.
I know how bikeable Paris is. It's the home of VeloLib, and I've already been sharing the marked bike paths with people on these rentals.
Last time I was in Paris with a bike was in July 2010, and I rode fully loaded from La Villette, in the 19th Arrondissement, basically the NW part of Paris to Versailles, via the Bois de Boulogne, which is in the SE part of Paris.
It was an amazing thing to be able to do.