My strategy for the European Heritage Days in Paris is to pick two "blockbuster" locations and do one each first thing in the morning on Saturday and Sunday. I get in line 30 minutes before they open. After that, I pick one or two areas nearby and visit what sounds appealing (or where the line isn't too long). Part of the joy of these days is discovering places you never knew existed. I'll never forget the former convent in the 6th that's now a school for the deaf where students led tours (in French and sign language).
I second the Senat (in the Jardin du Luxembourg) where you can also see the greenhouses, as well as the Hotel de Ville and Cour des Comptes. I also recommend the Palais-Royal where you can see gorgeous 18th Century decor in what are now government offices. There's a concentration of interesting things to visit in the inner ring arrondissements (especially 1-7).
You'll usually find articles that weekend of "top sights" to see, especially on websites like sortiraparis.com. Those tend to highlight places that are usually closed to the public (and will therefore draw big crowds). Really though, if you go with an open mind and spirit of adventure, you can't go wrong.
