The range of the French horn is very wide indeed:
Today, music for the horn is written in F and sounds a perfect fifth lower than written. The limitations on the range of the instrument vary according to the available valve combinations for the first four octaves of the overtone series and after that by the ability of the player to control the pitch through both their air supply and embouchure. The typical written ranges for the horn start at either the F♯ immediately below the bass clef or the C an octave below middle A.
The standard range starting from a low F♯ is based on the characteristics of the single horn in F. But there is a great deal of music written beyond this range, on the assumption that players are using a double horn in F/B♭. Its valve combinations allow for the production of every chromatic tone from two octaves on either side of the horn’s written middle C (sounding F immediately below the bass clef to F at the top of the treble clef). Although the upper range of the horn repertoire rarely exceeds high C (two octaves above the horn’s middle C, sounding F at the top of the treble clef), skilled players in a good symphony orchestra can achieve yet higher pitches.
It was once the case that notes written in the bass clef were written a fourth lower than the required pitch instead of a fifth but this is no longer the case.
In its middle range (most comfortable range), the French horn is capable of a great deal of expression especially when playing a simple melodic passage. Probably one of the best ever examples of this would be the andante of Tchaikovsky’s Fifth Symphony.