Should that game be hearts of iron 3, where everyone got a very limited number of divisions (compared to Germany 1000+ divisions in HoI IV), navies takes years to build (not like IV where we can build 2 carriers a year quite easily) and where the AI is quite cautious, then Vichy being at war with the Allies would totally make sense.
Vichy would start with all the french colonies under control and at war with the allies, and the allies would grab some of these colonies slowly with time passing, having much more important problems to deal with, like the war in north africa, or in asia.
Since HoI IV naval battle are way too much decisiv (by that I mean I've never seen a draw, each time, one navy utterly destroys the other with almost no loss, or there is no battle because one of these fleet just escape before fighting) you couldn't model the "small scale battles" involving at maximum one or two capital french ships against three or four british capital ships.
Between Vichy and the Allies, it was not a total war that was fought, more like a border war (Commie China and Nationalist China in HoI IV). However, having Vichy being totally neutral would still be a bit weird considering the number of fights that happened and the material loss of such battles.... As much as the material gains for the allies, an insane amount of auxiliary ships, and even some capital ones.
