Most Americans employed here were sent by their U.S. companies who applied for and secured their visas before they came. That's the best and easiest way. Others came here as students on a student visa which allows working up to 20 hours a week. With luck, the others find jobs where the employer is willing to get the visa for them. There is also a large number of Americans who manage to work here in Paris for employers located in the States or elsewhere.
Writers are among the group journalists, guidebook authors, novelists, etc.
Also, photographers, film and video producers, researchers of all types, etc. The third year in Paris I gave up and stopped looking and started doing. I took a volunteer post at an organization as the public relations director which exposed me to the community and helped me network. I headed a committee to develop a Web site for an anglophone organization. You can, too.