There are many free resources when job hunting in Paris for a job that will use your English speaking skills and knowledge of the U.S/anglophone business world. I have tried here to put these together for you - one stop shopping as it were. If anyone knows of any other useful tricks - please add them.
Getting a job in France is difficult for two reasons 1) French unemployment levels have rarely dipped below 10% in recent years 2) If the job isn't given to a French person, then it will likely go to a European who already has papers and is possibly already living in the capital.
BUT! As a bilingual American who is savvy in both the French business and cultural worlds as well as the U.S. business and cultural worlds - you have something unique and desirable to offer. While most Europeans speak English fluently (sometimes better than we do...) it is rare that they know the ins and outs of our business world & business practices and can parlay with top CEOs the way a native can.
The easiest way to get a job in France (Paris) is through a U.S. firm that sends you there as an ex-pat. Secondly, is to go there and look for jobs with U.S. firms based in Paris.
There are a myriad French-American associations, foundations, resources etc in Paris that are available to you either for free or as a result of some creative thinking and internet research. Lists of companies and contacts are posted in a lot of places - you just have to look and then send away your CV.
American Chamber of Commerce in France sells a list of U.S. subsidiaries (filiales) as well as mentions the names of its board members online.
American Chamber of Commerce to the European Union (idem)
U.S. Embassy in Paris - Commercial Services - one of their roles is to sell a listing of U.S. subsidiaries based in France.
FUSAC - free newspaper on the street as well as website that lists job posting for bilingual (English, French) speakers.
American Church in Paris - go to their website or visit the actual church for postings on jobs, babysitting gigs, groups... whether you are religious or not this is a great resource.
FPA - Foreign Policy Association - has a job board that groups job listings (involving foreign affairs) worldwide - www.fpa.org
FUTURESTEP - job board that posts positions worldwide and has posts for both the public and private sectors - www.futurestep.com
USAJOBS - official job board of the U.S. government, lists jobs worldwide including Departments of Commerce and State (there is a foreign commercial service officer exam) - www.usajobs.com
European American Chamber of Commerce - sells lists and has job postings/company expansions and other news regarding U.S. firms in Europe - http://www.eaccfrance.com/
UNIVERSITY ALUMNI CLUBS - don't overlook alumni connections, lots of universities (NYU, Columbia, Cornell...) have a France chapter and could serve as a good contact.
UNESCO - www.unesco.org
TALENTS.FR - don't forget recruiters (while most may require working papers, some don't)
Lots of French companies allow you to build a profile on their website and/or apply to jobs via their website e.g. LOREAL, CLARINS... many of these large French corporations will be interested in your profile. While time consuming, this can have great results!
While jumping the hurdle of not having papers will be tough, if you have a good work experience background and have honed your CV and lettre de motivation writing skills, speak French fluently and know how to sell your specific skill set - there is no reason why a French company wouldn't want you. You have something that they cant train their staff on (25 to 35 years of being a native and all that goes with it - having worked in the U.S., having a U.S. degree and the ability to bridge the cultural gap and relate to clients stateside).