Not sure if you're still following this thread, but here's some information.
To acquire a basic visa, you'll have to provide proof that you can support yourself and have insurance coverage for a year even if you are not working. If you haven't already done so, you should go to the Consulate of France website nearest you and investigate their requirements. It takes time, a lot of paperwork and a fair amount of money.
You won't be allowed to acquire a work visa unless you have already been hired in Paris.
If you can possibly visit before moving here permanently, you could make the rounds of the language schools and possibly get a job as a business-level English teacher. The other option would be just teaching basic English. Then you would have a work contract to present to the Consulate - though you would still have to prove that you could support yourself for one year. Don't expect good working conditions or good pay, though. If you are paid by check, your income will be taxed in both the US and France.
If your university has any connection with one in Paris, perhaps their personnel department could advise you. However, French law demands that if a French person can do the job, a foreigner cannot be hired.
Many people who enjoy creative writing start blogs with paid advertising. However, these are extremely time-consuming and won't guarantee anyone a living wage. They are also a dime a dozen, and unless you have a lot of experience with coding, and have a really unique angle, you won't get much traffic.
Some people take jobs in the US which allow them to work anywhere and be paid in the US. If you can make enough money doing this, it can be a good option, but you'll have to find a French bank which will work with you.
A lot of people hope to find a soul-mate, fall in love and have their problems solved. Getting into a relationship in France is easy, but getting out of a relationship in France - either PAC'sed or married - will leave you with zero.
As far as trying to find a long-term apartment in Paris, it is almost impossible for foreigners, and especially Americans.
You'll need to prove that you are working in France, can pay 4 times the monthly rent, have a French bank account, and pay taxes in France. If you cannot pay 4 times the monthly rent, a bank guarantee from a French bank is your only other option. This means that one year's rent will be blocked in a separate account, while you continue to pay monthly rent throughout the year. Priority always goes to French students, roommates, and families with children, because they are seen as a safer option.
Sorry to give you such a harsh reality check...