Heat milk in a medium saucepan until warmed through- but do not boil. While the milk is being heated grind the coffee beans in the coffee grinder. Add the freshly ground coffee to your French press. Add 3 1/2 cups of hot boiling water then add the lid/filter assembly. Let it steep for 3 to 4 minutes then slowly press the plunger down in a steady, even manner.
While the coffee is steeping, remove milk from heat and set on a kitchen towel on your counter top so it's on a slight angle. Set an immersion blender in the shallow end of the pot and froth the milk on high speed until the foam holds, about 2 to 3 minutes blending on high. Divide the coffee out amongst the cups and spoon the frothed milk on top of each. Serve immediately.