First point is that if you work in France, you are supposed to be affiliated to French “social protection” system. That entails paying income-dependent mandatory contributions but also benefits (health insurance, retirement pension, unemployment insurance).
If the US company you're working for does not have any legal entity in France, you are in the case of a firme étrangère. The company should declare your status and pay their part of tax. That might require some efforts on their side to deal with the French authorities. The process is described (in French) in the linked page.
If the US company has a legal entity in France, that entity should be your employer.
Now, if you are not a permanent employee of the US company but a freelancer/contractor, it is your duty to setup a legal framework in France that allow you such freelancing. First point is still valid. There are several ways to setup such framework, the simplest one being auto entrepreneur, but it depends on the annual turnover you get from this activity, and various other issues.