To put it bluntly, you’re in a pretty tough spot here. There are obvious problems with the three scenarios you mention:
1. What you are describing here is a “visitor” visa. (A “long stay” visa is a visa granted for more than 3 months – whether or not there are work privileges attached, which is a whole other question.) If you work remotely of France, you work IN France and must be duly registered for taxes and “contributions” (social insurance). If your employers have a French office, they might transfer you to be on their French payroll – but most US employers won’t take this into account because social charges (i.e. contributions) are considerably more expensive on the employer’s side than in the United States.
2. Ideally, at your age, this is the way to go. However, do you speak French? Are you both in transferable professions in France? (Most medical qualifications are difficult or impossible to transfer, although sometimes you can work in a related type of job in industry.) And basically, for an employer to hire a foreigner, they usually have to prove that couldn’t find anyone. already able to work in France and sufficiently qualified. The exceptions to this rule are mainly technicians in demand (in fields where there is a shortage of French candidates or EU nationals).
3. There is an ‘entrepreneur’ option under the ‘Talent Passport’ category – but as you say, they are not looking for people who create bed and breakfasts, but rather ‘innovative’ business plans where applicants have a serious track record in the type of business they offer. (The idea has generally been that foreigners “bring something” to France or that will benefit France – new technology, a new way of doing business, etc.)
Buying a property (other than as part of a business plan) really has no effect on your ability to get a visa. There are no special restrictions (or advantages) for foreigners owning French property (as long as you pay all the appropriate taxes and comply with the various rules that apply to property).
Yes, these are generally the main categories of expats here in France. France is not really interested in attracting people who want to “start a new life”. Unless, of course, you have a talent or ideas that could benefit France.
It is also not so easy to change the category of residence permit once there. So it pays to do your planning in advance. You don’t have to reveal any personal information here on the bulletin board, but consider what your professional qualifications are, what your level of French is, and consider the likelihood that you can find a job here in France. You will need to study the job market and understand the French “obsession” (or so it seems) with formal qualifications and how to present them on a French CV (which is more like the American CV). Or, if you want to go the “entrepreneurial” route, you should study the French market to try and come up with a business plan that meets some of the needs of France and French society (and maybe creates a bit of a employment for local French people).
I’m not trying to be negative here – just very realistic. Think about why France, in particular. France can be an aggravating place for those accustomed to the “Anglo-Saxon” world (especially in terms of work, labor law, regulations and taxation). I happen to be married to a French citizen, but even then the first few years here were difficult. You couldn’t drag me out of here – but a lot has changed in the 25 or 30 years I’ve been here. Think very carefully about what you are trying to accomplish by doing this kind of thing.