Aaah so basically if we get married and he gets here we just have to apply for the carte de séjour? Aren't there any requirements of a sufficient income that we might run into? Or anything else? Because it sounds too easy actually.Don't confuse a visa and a residence permit (or in France, a "titre de séjour", usually a carte de séjour). The visa only gets you into France. Once you're there, you then apply for a titre de séjour so you can stay.
In your case, the "long stay visa for non-professional purposes" (the "visitor visa") is for someone coming to France for some reason other than to work. You're not allowed to work on that type of visa, and to get that sort of visa you need to show that you have the resources to live in France for the duration of your proposed stay without resorting to working. Your boyfriend would also have to have a private health insurance for the year, roughly equivalent to the French health care system (but probably with "medical evacuation" coverage so he could be shipped back to the US in the event of serious accident or illness).
Since you're not a French citizen, he's not eligible for a spouse visa. But, the good news is that, if you were married, he wouldn't need one. The spouse of an EU citizen can apply directly for a carte de séjour if he is coming to France to join his EU spouse who is exercising her EU rights. As the spouse of an EU national, he would have all the same rights you have in France, including the right to work.
He could enter France on a Schengen tourist visa (i.e. the stamp in the passport that lets you stay for 90 days) and he would have to apply for the carte de séjour within the first two months he is in France. You would have to show that you are living in France and it's actually much easier if you've got a job or can show that you are studying in France (i.e. exercising your EU rights).
If you're not married, then things get really tricky. To get PACS'd you'd have to live together in France (with him on some form of long-stay visa) for either 6 months or a year - and at that point it's unclear whether he'd have the same rights as a spouse with regard to a carte de séjour. (European regulations get interpreted differently by different prefectures.)
If he could find a job in France, he could get a work visa, which would give you a bit more time to decide whether or not you want to get married.
I'm sure if there are other options, someone will pop in here with suggestions.