It's rather unlikely they'd even try. France has been a united country for a very long time, and any enforced division wouldn't last long, even if anyone would consider it.
I don't think Germany wanted a partition or would have been able to implement it. Britain would have maintained an eternal blockade to prevent Germany from partitioning France and I don't think there was much political will in Germany to do it either.
Some annexed areas, demilitarized zones and harsh concession in the peace treaty are a likely scenario.
Not at all.
The problem with dividing France is keeping it divided. If five year after you leave the ''French patriotic party'' of Aquitaine win elections and re-unite with France, what do you do ? Send occupation troops again ?
OTL France was strained by occupying the small region of Saarbrucken alone, Germany could not enforce its division of France.