I think the nicest thing about Paris is just wandering - especially as you have so little time.
If it were me I would take the line 4 metro (purple line) direction Porte D'Orleans to Cité on the Ile de la Cite. Then I would wander through the Ile de la Cite and Ile St Louis, soaking up the atmosphere. Admire Notre Dame but don't bother to go inside on a weekend, it's too crowded to appreciate the atmosphere. Riffle through the stalls of the bouquinistes (the booksellers who have boxes along the side of the Seine)
Have a Bertillon sorbet or icecream on the Ile St Louis. These are truly among the best in the world - the cassis is like having a million blackcurrents explode in your mouth. There are several places on the Ile St Louis, many just by the bridge that crosses to the Ile de la Cite.
Then I would cross north over the Seine to Hotel de Ville and have leisurely late lunch in the Marais, the area just to the north of Hotel de Ville. There are many fantastic restaurants there. If you have spare time (which I doubt) the Picasso museum is just up the road.
Then I would get on the metro at Hotel de Ville on the ligne 11 (brown line, direction Marie de Lilas) change at Republique and take the ligne 5 (orange line, direction Bobigny) back to the Gare du Nord.
That would be my plan - you have hardly any time at all so you don't want to waste it rushing around from attraction to attraction, just enjoy what Paris does best - food, drink and atmosphere.