Renewal of Long Stay Visiteur Visa...

The best for you might be to register in a french university, this could help a lot to get your long-term VISA

It's strange that they'd schedule your appointment for AFTER your visa expires. I live in Seine Saint Denis (where we don't have online options), but here you go to schedule an appointment (which is always before expiration) and then they give you a récépissé (a receipt) showing that you've submitted a renewal application. It serves to show you're legal even after the visa expires and until you get the new titre de séjour. For instance, for me, I went last year in May to schedule an appointment, which was in July, and then I got a récépissé valid until October 18, proved I was legal between visa expiration on August 16 and October 18.

As for enrolling in a university, that might help get a visa, but it won't help you with this particular problem, of course. This is one of timing.

I would suggest calling the préfecture, if you can, to check on this. You're probably right that you can go and come back on the 90-day rule, but it's just odd that they scheduled your appointment to submit the renewal application AFTER expiration of your visa. You didn't get some kind of "récépissé" from the website when you scheduled the appointment did you?

Fingers crossed for you ... I know how stressful this can be!