Hi and welcome to the forum.

Well, as a UK citizen, your girlfriend has every right to come live and work in France, so that's the easy part. AFAIK, there is no need to declare herself resident at the mairie. For the PACS, you will have to declare where you both are resident together, so that should be adequate - but I believe that is part of the PACS paperwork and not something she needs to do on her own.

I suspect she can still register with La Pole d'emploi (which is what ANPE/Assedic is calling themselves these days), but whether she is entitled to any benefits is doubtful if she is voluntarily leaving her job in the UK. I don't think La Pole d'emploi will give her French lessons, but they may know some of the providers of language training in the area. Her chances of finding work are fairly slim until she can speak French at some basic level.

For the carte vitale, she needs to have a form from the UK showing that she has paid into the UK system for some period of time. (Independent of the PACS.) Once you are PACS'd, you can see about putting her on your carte vitale (as a dependent). I would check with the mairie where you are doing the PACS.
Cheers,
Bev