Hi Deborah, welcome aboard.
Generally as I understand it, the spouse of a non French EU citizen is entitled to reside with them in France without issue. The Carte Sejour is effectively a "Residency Card" which confirms your right to residency within the country. As I understand there are two types of Visa requirements to enter the country, being SHORT stay(up to 90 days) or LONG Stay(usually 12 months and renewable with a Carte Sejour).
You do not need to apply for a Visa to enter France, but you may require a visa if you intend to stay for periods longer than 90 days in other Schengen countries.
I also was of the opinion that you could only apply for the Carte Sejour once in France via OFFI, which is the equivalent of their Immigration Dept.
Carte Sejour's are often "renewable" meaning that you have to renew the application every year. This may however, not apply for the Carte Sejour for the spouse of an EU Citizen. We are here on Long Stay Visitor visas as we do not have any EU alignment. As such we have to renew every year, but after 5 years we can receive "permanent residency"
The AE status is an abbreviation of "Auto-Entrepreneur". This is a form of self employment whereby the administration and tax regimes are meant to be a little easier. Some people say it works well, others still have issues.
I would think that if you are only going to be here for a couple of months at a time, that you may not require the Carte Sejour or the AE, but perhaps worth checking with the French Consulate.
Brush up on your french either way..........it will help.