The german player have the choice to create Vichy or not when France surrender. So it isn’t a “handicap” for him like you say, because he can choose.
For me, Vichy France is not an handicap :
-All Vichy’s income is collected by germany (rule 14.4.2, page 60).
-Vichy gets a free recruitment roll of “2” each turn (as long as Vichy posses Corsica and Southern France, its capital) until he is aligned with germany (when the allies or commintern declare war on Vichy, if they are also at war with germany, something that should happen every games).
Remember that free france and vichy france are in a “civil war” = free france can’t declare war on Vichy because they are alredy in conflict. So, Free France can’t align Vichy with Germany.
-Like I said in the previous paragraph, vichy could become aligned (= annex) by Germany.
-Also, the german player can decide to lend lease Vichy France (rule 14.4.3, page 61), when he control it.
So I think that he can build a factory and place unit for vichy ? Need to be confirmed.
I Think that the Anton Case is represented with the annexation of Vichy by Germany, when he is aligned.