I've recently converted to Movnat (I know they are different things, but Movnat stemmed from methode naturelle) due to several reasons. For starters, I find bodyweight repetitions boring (Never started weights at all) and would much prefer training upper body strength in a more interesting way. I'd rather climb trees and swing about in them than go for maximum pullup number.
Secondly, it's the way we were meant to exercise. Our ancestors never adhered to a strict routine, they got their exercise through this, not because they wanted to, but because they had to. That said, make sure you can at least pull yourself up on a branch before beginning to climb trees, i.e. have some strength before you begin.
Thirdly, injuries are avoided. our bodies were designed to move this way; it's what we should be best at doing. Overuse injuries are almost non-existant, as if you get tired of running, you start climbing or crawling. Completely different movements. Other injuries are also greatly reduced, as the muscles learn to work together. And I'm not just talking about certain arm muscles. When crawling, your arms and legs learn to work together, and so on.
I think the natural method is better than weights for these reasons. Besides, if you absolutely cannot give up weights, Movnat involves lifting, carrying and throwing anyway, which is much more fun. If you honestly only care about looking good, continue, but remember you are giving your own training up for other people's attention, rather than your own personal health.