Both incorrect in the light of my 1.3 experience. Individual outcomes don't really prove much. Correlation does not prove causation unless you can isolate the possible causes and, by repeated testing, show a different outcome when the thing that (supposedly) decides it goes one way during one try and the other way during an otherwise identical try.
I did some semi-scientific testing of it on the fly in my current German game. I had edited away the Vichy event, the resulting being that France will behave just like any other country when collapsing.
First time, France went over the surrender threshold when I captured Paris. However, while I was mopping up Poland, Italy had made impressive progress on its front against France. France surrendered to Italy, which held more territory in raw number of provinces than I did. I reloaded and repeated, and every time, the same happened.
Ergo, it is not random. Neither does it depend on who takes the "last" VP.
Second time, I didn't take Paris when I could, but surrendered it. Rest of my army surged forwards to grab as much land as possible, expecting that whatever I wouldn't grab, the Italians would get. After having taken pretty much what I wanted, I finally took Paris. This time, France surrendered to me.
I'm not entirely positive I had a bigger occupied province count than Italy, I didn't do a full province count. It's quite likely though just looking from the relative sizes of the grey and green blobs.
The hypothesis that would best explain my observations is that raw biggest number of occupied provinces is what matters, but I don't claim positive proof for that.