Consider a (so far hypothetical) situation like this: Jack is a non-French EU citizen living in France. Jin, his spouse, is a Chinese citizen. She has a French residence card (titre de séjour directive 2004/38/CE) as spouse of an EU/EEA/Swiss citizen.
My understanding from this page is that she cannot travel within the Schengen area unaccompanied by Jack. Is this correct?
Now the main question: Jin travels to China alone and has a return ticket back to France which involves a transfer through Germany. Does she need a visa to return? If yes, a visa to which country? Please consider both the case of single ticket to destination and separate tickets for the two legs of the journey.
I find the linked article a bit confusing. Also, the example it presents about travelling alone is to a non-Schengen country (Cyprus). I would appreciate it if you could back up any answers with appropriate references. It's always good to know what to reference when needing to clarify things with a checking desk or border control.