|Old Hat Makes You All That|
My greatest trick when developing my own method of playing the French Horn was devising a scheme of intutive fingerings that allowed me to play with good sound on both sides of the horn and hit the right notes.
Before valves, French Horn players knew that the key of the instrument had a great deal of effect on the Horn. High Bb was shrill, F was very mellow but slotted poorly, Eb was worse, and bass C had an excllent sound. Thus, composers would write their music with the sound of the Horn they desired in mind. This can be exploited in the modern day in two ways.
1st Method: Key by Fingering
If F sounds better than Bb, and C sounds better than F, then you can use the appropriate fingerings to generate those sounds when appropriate. Bb side becomes F when playing 13, thus T13 is a better fingering for low C than T0. F becomes C when using 13, thus 13 is a better fingering for low G than 0. These are very obvious and you can try it yourself! The best part of this is that the Horn generally does not inherit the slotting of those keys in normal playing, so you can do this with great success as long as you don't intend to go overboard with it. Using 13 on the F side for every note is a bad idea.
2nd Method: Key by Pattern
The reason you don't necessarily inherit slotting by fingering is because you also inherit it by the pattern you are using. The French Horn is a unique sort of beast and it slots best using fingerings that existed on the same note an octave lower. Using a fingering for the first time it shows up (such as 1 for middle C) is generally a really bad idea. If you've learned from a French Horn fingering chart, then don't throw it away, but grab a Trumpet fingering chart. You need to know normal fingerings anyways. First time 1st valve fingerings are some of the worst because they fit the Eb pattern which is a notoriously poorly slotting key. Avoid using first valve for anything but F and Bb on the F side.
My Fingering Chart
This chart shows my personal fingering method for French Horn and notes. Keep note of the overlaps and ranges where each side of the horn isn't suitable. There are times where F or Bb side of the instrument should definitely be neglected, but you can see that a full high school caliber range is possible with either. Middle C means the middle C written on the staff.