ORIGINAL: eriador08
To 7: If you decline Vichy you get the chance to annex whole France with big parts of their colonial territory like Algeria, Tunisia and Syria. This can be very handy, if you want to secure the Mediterranean anyway. You get also a better chance for a axis Spain. There is even an event for this purpose. You need to take Algiers to finish France off though, since they will move to Africa and fight on from there.
After running an Axis playthrough, I now think conquering southern France is in fact the better approach for my play-style. You do get a decent chunk of MPPs for that time frame; and I have a far easier access to the Mediterranean bolstering southern Italy.