I was just in Paris for a week with the family and had a great time. This was my third visit and we went low cost on the food an had no problem eating well on cheap while enjoying it all. Too funny that you mention Le Relais de l'Entrecôte. We had dinner at the on on Monparnasse and enjoyed it. They had the best fries I have ever had and great desserts as well. Its been 14 years so I was surprised by the number of pizza and sushi places.
We did all the touristy things (Catacombs included) and was most surprised and impressed with Les Invalides (Museum De Armee and Napoleaon's Tomb). I hadnt been on the first two visits.
If you have Comcast search for Anthony Bourdains recent Paris visit with Eric Ripert. They hit a number of new Bistros that are breaking the mold of the typical high end Paris eating experience.
I was bummed there wasn't any auto museaums in Paris, like Torino, Munich, etc but if you'd like to do a sporting type of adventure I would try to hit a local Rugby or football match. There are a number of clubs in the city (Racing Metro, Stade Francais, Paris St. Germain). If there is a match at Stade de France, it would be an experience.
Stade.fr
PSG.FR - Official site of Paris Saint-Germain
Racing Métro 92 Rugby - Depuis 1882