Using heavy cream vs whole milk
I don't think the type of milk you use would contribute too much to the fluffiness. The eggs in the crepes is what makes them fluffy in my opinion, the more eggs you add the fluffier the crepe. To make a lump-free batter, mix it in a blender till smooth.  

Let batter rest for 20 or 30 minutes in the fridge to relax the gluten in the flour.  You should have fluffy crepes, just remember the more eggs you add, the more flour you will need, and don't make the batter too thick, it should be about the consistency of stirred yogurt.