title_body: Fine-grind French Press - Sacrilege? Better method?
upvoted_answer: I just want to preface by saying that while product recommendations are frowned upon here in general, there is a certain necessity in a stack like this where brew methods are often tightly related to brands.
  
  There are a couple options here, the first being modifying your french press a bit and the second being a different brewer that may be easier for attaining your goal. 
  
  As B540Glenn mentioned, you can try cutting our a paper filter into a circle and putting it next to the mesh filter in your french press. This will get rid of a lot of the grittiness and a little bit of the oiliness but will keep your big body.
  
  The second option is to try out a Clever Dripper. It combines what you seem to like about immersion brewing and combines it with a paper filter that drains into your mug when you're ready. It's a simpler and faster way of achieving what probably is a similar result to the french press with paper filter method.
  
  Hope this helps!