Consequently I didn't find much difference when I went GF other than the fact that I dropped a bit of weight. Gluten also is avoided by some pro cycling teams whether their riders have CD or not because it helps with recovery due to a reduction in body inflammation levels.
If you want to address fat levels, then look at reducing carb intake and replace with good fats and protein, although obviously don't then take in a higher number of total calories. Right now, I do rowing and weight training (the weights are good as we age as it helps bones/muscles/hormone profile) and use carb intake to manipulate how I look over time e.g. if I want to bulk up and support muscle size and strength gains I'll worry less about carbs, but when I want to get more defined I reduce carbs. cheers.