Using a French press with finely ground coffee
If you use immersion brewing (which is what a French press does) with more finely ground coffee, you will want to reduce the time as extraction is faster.  I wish I could give you an exact time, but I have not experimented with this; I would start with approximately 2 minutes.

You are also likely to ge ta muddier, grittier cup as the mesh in the press will not catch all of the more finely ground coffee.