Yes! Finely ground coffee brewed cold can have a slightly bitter taste, and is more likely to sneak past your French press filter resulting in grainy cold brew. Both of these things can be fixed, however! To keep more finely ground coffee from sneaking through your French press's filter, you may want to drape a coffee filter over the mouth of the French press before you depress the plunger. For a less bitter cold brew using finely ground coffee, Coffee Craft Code advises shortening the brewing time by "25 to 50% when using finely ground beans" suggesting "anywhere from 6 to 16 hours." You also don't need quite as much ground coffee if using finely ground beans — I'd recommend 1/2 cup to 3/4 cup per 4 cups of water.