I recently married a man from France who and I am interested in applying for a french passport. What is the procedure in order to obtain dual passports? Do I need to apply for dual citizenship? What should I know?

You can't "apply for a passport" you can apply to become a permanent resident and have the right to live in France. He will have to sponsor you to move to France as a permanent resident, this is by no means a quick process. In most countries it can take a few months. Once you are apporved to live in France as a permanent resident you have to wait a few years (living in France at the time) to become a citizen, once you're a citizen you can be issued a passport.

I have no intention in living in France. Do I have to be a French citizen in order to obtain a French passport?

Yes, you can get a french permanent resident visa put in your US passport and have the right to go back and forth, but only naturalized citizens receive passports.