Not being married is, in some ways an advantage. If you were married and both of you were Americans, you could get a visa based on only one having a job offer - but the "trailing spouse" would get a non-working residence card unless they could also line up their own job before applying for the visa. If you were married to a French person, you'd be entitled to a visa, but with working privileges deferred for a year or two. (It keeps changing.)

If you aren't going to be working, you will need a reason to move to France. (And adequate resources, including health insurance.)
Cheers,
Bev