Here are three apartments where I have stayed in Paris. They are much less expensive than a hotel room, and I save money by being able to make my own food. One of my joys in Paris is going to the local groceries and outdoor markets. I love to immerse myself into the local culture of wherever I travel and an apartment takes me out of the hotel 'tourist' environment and into the 'live like a local' mindset.
Most apartments offer free wifi and phone calls to America.
Don't miss out on a trip to the Monoprix, it's like a French Target with groceries, but so much better.
I am a big fan of apartments for a stay longer than 4 days. I haven't used Air BnB, so I have no personal knowledge of the service, other than some of my friends stay in them. I prefer going through a rental company or stay in smaller BnBs and Hotels.
There are good deals out there, you just need to search.