Annual Museum Passes
The first month I moved to Paris I bought an annual Musee d'Orsay pass. I only used it once because the d'Orsay isn't big enough to require multiple visits. Nor did I care for their collection. But I had it if I ever needed it.
I thought I had already made a post about the annual museum passes but I guess I didn't so here it goes. There are a few museums around the Capital that offer an annual pass. Musee d'Orsay is one, but so is the Louvre, which makes more sense to me because it's such a big museum. I purchased my year pass for 80€. You can also also get the Duo (2 personnes) for 120€. I really recommend shelling out for it. If you purchase the Louvre pass you can get discounts on other annual passes, which gives it another reason to have.
The Laissez Passer from the Pompidou is one such. I didn't care for the Pompidou so I wouldn't need more than one visit. But if you're planning on having a cache of museum passes it's not a bad idea.
For reference The Picasso Pass is another. Apparently the Opera de Paris offers one too, but all I can find are the passes for shows. The Pass Quai Branly is here. The Palais de Tokyo's Tokyo Pass is here.
I'm really surprised Invalides doesn't offer an annual membership. For now they only tout the Membership Pass which to me is a ripoff. No one can do 20 museums in one day. Museums themselves aren't expensive enough to need to spend 40€ on something you'll probably only get two uses out of.
Another way to save is applying for a ICOMOS membership. It's tax deductible so feel free to write it off. It's $210 a year for the international membership, which is steep. But their list is pretty impressive. My only gripe is that it's only valid from January 1st to December 31st, no matter when you buy it. And if you happen to buy it after September you won't get your card until January. It ships from Paris so it can take 6 weeks to get to you (if you live elsewhere). It's something to think about when travel is truly unrestricted because you'll want to use that pass at very museum you can.