I hope that you don't put down the saxophone, but I really enjoyed playing the French Horn, the biggest challenge was lung capacity and now how to fill your lungs all the way between notes. As this is a late reply I'm sure you have had a little more experience and know what I'm talking about.
Fun fact; The first French Horns didn't have valves rather the had interchangeable crooks which moved the instruments range along the scale. So in order to change notes you had only your embouchure and diaphragm. And to help train these muscles and my skill I was instructed to attempt my scales with out using the keys, and only my muscles. I enjoyed that challenge. I bet you might be able to do the same with the Saxophone, but I would imagine that it isn't as necessary. Though I have yet to learn to play the Sax. But the French Horn there are a few note changes like C to D played on a F Horn was mostly a embouchure adjustment. Also if you aren't aware there are difference size mouth pieces and different companies feel different, so if you can try out a few different ones that might help you out.
Have Fun I hope to hear about your experience, and I am also curious about why you switched or choose to add the French Horn to your repertoire.