The name of this instrument can be confusing, since it's commonly referred to as the "French horn" -- but only in some parts of the world, and generally not by the people who play it. However, to quote Ron Boerger's Horn FAQ (see below),
It's a sad fact, however, that in the US, outside of the music community, telling someone that you play horn will usually elicit a "Oh? What kind of horn, trumpet?"-type response.
The horn is considered by many to be the most difficult band instrument to master, and, perhaps as a result, capable horn players are generally both difficult to find and in great demand.
Concert band arrangements generally include at least one, and often as many as four, distinct horn parts.
Here's a collection of pointers to various places in the Web that discuss the horn: