First of all, congratulations! An assignment to Paris is something to be proud of.

To take your questions in order:
1. Cost of living. There are a tremendous number of COL calculators on the web, but personally I find them kind of misleading. What's important to know is whether you'll be on an "expat package" or on the local payroll.

With an expat package, the company generally tries to keep you even with your Stateside salary and taxes (often including someone to do your taxes, which get complicated when you fall under two jurisdictions as you will). With an expat package, you retain your US pay (usually) and have certain allowances paid for housing, trips home, etc. They generally continue your US based health insurance and continue to pay into US Social Security for you. (Doing so exempts you from paying French withholdings for a certain period of time, provided they are planning on transferring you back.)

Under a local payroll arrangement, you're paid just exactly like anyone working for the company in Paris (with French social insurances, retirement, etc. taken out of your pay) and the company doesn't subsidize your accommodation or other typical expat benefits. If they are transferring you "permanently" it could be an advantage to go onto the local payroll right away.

2. To find an apartment fairly quickly, you want to get to know FUSAC - it's a free want-ad publication that's available in most English-language bookshops and other hangouts in Paris, and it's available online France U.S.A. Contacts: cultural exchange between France and the USA

They have a variety of rental agents - for both furnished and unfurnished flats - and the agents are used to dealing with Americans (and Brits). (In fact, many of them ARE Americans or Brits themselves.) Rents are steep in Paris (as in any major city), and most newcomers are startled to discover how small the apartments are here. But if your company is subsidizing your housing, they may be willing to set you up with a rental agency or even a relocation expert who can help you get settled in.